Short of your "Oops All Spells"-esque combo, I don't see many ways for this deck to actually win. Against Junk you're running a bunch of mediocre creatures that support your theme while your opponent is playing the best creatures in the format. You don't have enough disruption to stop Twin and Infect (or Ad Nauseam, Scapeshift, or any other combo deck), and you don't have the tools to stop Affinity or Burn from racing you.
You could replace it with something like Violent Outburst though. It's bad, but at least it's legal.
I can't see why you'd want to do this. Not only is Violent Outburst a terrible card, it reduces the number of cards in the deck that Collected Company can hit, and since the deck is built around Collected Company you'd want to avoid doing that.
If you're willing to splash (which may not be worth it) Serra Avenger is another undercosted beater with a drawback you can ignore. Priest of Urabrask is another ritual creature like BTE (albeit not as flexible). Arbor Elf is probably better than Llanowar Elves since it can untap your Stomping Grounds to get red as well as green. Aether Vial also seems like it would be good here--if you set it to 2, you can get free mana (BTE) or instant-speed uncounterable fatties.
Why are you running Duress instead of Thoughtseize? Being able to hit creatures seems important, especially for a deck whose wincon consists entirely of them.
Unless burn is upward of seventy percent of your meta, I'd highly recommend against mainboarding Leyline of Sanctity. It's a dead card in a lot of matchups and you'd wish you had something else. I'd also recommend Kor Firewalker or Timely Reinforcements as possible alternatives to Leyline against Burn--Timely Reinforcements especially, because you can bring it in other matchups as well.
I'd recommend posting this stuff (discussion of sideboard tech and strategy) in the Knights thread since that's where most of the discussion about the archetype takes place--more people will see what you see there.
If you're just looking for a deck that plays Mutavault and Aether Vial I'd look to Merfolk. It's competitive (one of the top ten most prevalent decks in the format, and consistently rated as tier 2) and is likely cheaper than whatever you were looking at since it doesn't play swords.
There is some literature on a less competitive Modern knights deck that plays Aether Vial (link) if you're intent on playing that tribe.
EDIT: The link you just posted seems to be exactly the one in the Knights primer I linked to above. There's tons of info on the archetype there.
You're running too many Mountains and not enough fetches. Burn typically runs 7-8 mana producing lands (usually 4 Mountain, 3 Sacred Foundry, 1 Stomping Ground) and 12 fetches (typically a playset each of Wooded Foothills, Arid Mesa, and Bloodstained Mire). This is pretty important because you need as many of your draws as possible to be live.
Losing out on Boros Charm seems big and I'd look for away to slot it back in. You could probably cut down on the Skullcracks (since Atarka's Command is basically a strictly better version) and maybe one or two Searing Blazes.
I'd highly recommend against cutting any Eidolons. They're extremely powerful against most of the top-tier decks in the meta. You really shouldn't care about how much damage you're taking from them since you'll be dealing more to your opponent.
EDIT: Also, Exsanguinate should gain you the same life, but do twice the damage.
I didn't catch that you were talking about casting it with Sanguine Bond out--in that case, yes, it does.
I could see a white splash being useful here. It gives access to Path, which is a huge bonus. At that point, though, I'm not sure why you wouldn't just run Rhino and play Junk.
Not sure what you mean by 'scales better'--the cards result in the same gain in life, but Exsanguinate will always cost one mana more. Exsanguinate only scales better in a multiplayer game. I'd argue that Exsanguinate as a single card does more than what this deck tries to grind out with Stream of Life, Sanguine Bond, etc. but the OP seems to be wanting to grind out advantages over the course of the game and removing Sanguine Bond for Exsanguinate makes most of the cards in the deck pretty useless.
OP: If you want to call this thread a primer I'd try to include alternative card choices and a matchup/sideboarding guide at the least. Primers are supposed to be relatively comprehensive introductions to deck archetypes, and this doesn't seem to quite do that at the moment.
This deck isn't Modern-legal. Blossoming Wreath was printed in Weatherlight and is not in the Modern card pool.
This deck seems completely cold to combo. Since you basically have no interaction, you'll be dead when Twin combos out on you on turn four. Since you're running black I'd highly recommend a discard package (some combination of Liliana of the Veil, Thoughtseize, and Inquisition of Kozilek). I'd also cut Doom Blade for better removal--in a format full of Siege Rhinos and Tasigurs, you'll want something that can hit black creatures. I'd recommend Dismember or Go for the Throat. Abrupt Decay also gives you some much-needed interaction against Junk, Twin, and Infect. I'd cut Leaden Myr for Birds of Paradise if you really want to be ramping, but I don't think it's all that necessary since you plan on playing a long game.
Your creature base in general seems a little loose. You're running a lot of indisputably bad creatures just because they gain you life, which really isn't the way to go. Tarmogoyf fits into almost any deck with green and this one is no exception--it protects you and gives you an additional angle to attack from if you can't find Sanguine Bond. If you can't run 'goyfs I'd recommend some number of Scavenging Oozes--not only do they fight opposing Tarmogoyfs, Snapcasters, and Lingering Souls, they synergize with your engine due to the lifegain they provide.
22 lands seems low for a big-mana deck. Nykthos doesn't seem great here--most of your permanents only give you one or two devotion. Additionally, it's legendary and you don't want to be drawing more than one of it. Keeping one or two would probably be okay, but you definitely want a set of Verdant Catacombs in here. Woodland Cemetery couldn't hurt either, especially since you're a two-color deck.
You'll definitely want something like Creeping Corrosion out of the board against Affinity. Choke is excellent against Twin and also hurts Patriot Control and Scapeshift.
This deck isn't Modern-legal. Counterspell isn't in the Modern card pool.
The first thing I'd recommend to improve the deck is improving your manabase. Shocks and fetches make for a much smoother and effective curve than taplands.Cruel Control is an established UBR deck that might interest you, and even if it doesn't it'd probably be helpful for you to take a look at its manabase.
The primary issue I see with this deck is that it's really slow relative to other combo decks in Modern. A deck that can kill someone on turn six undisrupted simply can't hold up against decks that can kill turn 4 or 5 through disruption (burn, twin) or decks that run a lot of disruption (junk, patriot, twin). This deck honestly looks like a worse version of infect--both decks win by pumping synergistic creatures, but infect only needs to do half the damage this one does and doesn't require an additional combo piece in the form of Fling.
This deck also is completely cold to Abrupt Decay and Path to Exile, as other people have mentioned. The issue here is that roughly 30% of decks you'll run into have those cards. Additionally, Remand and Cryptic Command (another ~10% of the meta) ruin your combo and leave you out of gas since you have no way to refill your hand or filter your topdecks.
If you're intent on trying to make this deck works, free Kiln Fiend triggers would speed you up a lot. Mutagenic Growth is excellent for this, and Gitaxian Probe gives free Kiln Fiend triggers and essentially makes your deck 56 cards. I'd also test splashing blue for Nivix Cyclops in place of Foundry Street Denizen. You want to be casting spells in this deck, not playing a lot of creatures, so I think you'd get more value out of Nivix Cyclops. It's essentially a harder-to-remove Kiln Fiend, which couldn't hurt, and splashing a third color in Modern is relatively painless.
It seems like you're incredibly soft to combo and burn. Both Twin and Burn can basically ignore your board and have you dead by turn four or five. Two Torpor Orb isn't going to be enough--I'd recommend a few Chokes or Spellskites to go along with it. Choke is also decent against Scapeshift, UWR, and Storm, so it seems like it'd be a good card to be running.
I'm not sure how seriously I'd take these analyses, given that all of the test games you've discussed so far have been against tier 2/3 decks. Twin and Scapeshift are the decks you want to be testing against for combo, and you definitely want test against Junk, Bloom Titan, UWR Control, Affinity, and Infect so you have an idea of how the deck fares in the actual metagame. Calling your combo matchup good because you won against a Polymorph deck seems like a bit of a jump to me.
Since player B declared blockers before player A cast Flying Crane Technique, player A's creatures are blocked and will not deal combat damage to player B unless they have trample and deal enough damage during the combat damage steps to kill their blocker.
Since Flying Crane Technique untapped player A's creatures, they can block during player C's turn.
This just isn't true. Mirror-Mad Phantasm, Stinkweed Imp, and Hedron Crab just can't compare to Tarmogoyf, Siege Rhino, Vendilion Clique, and Arcbound Ravager.
Short of your "Oops All Spells"-esque combo, I don't see many ways for this deck to actually win. Against Junk you're running a bunch of mediocre creatures that support your theme while your opponent is playing the best creatures in the format. You don't have enough disruption to stop Twin and Infect (or Ad Nauseam, Scapeshift, or any other combo deck), and you don't have the tools to stop Affinity or Burn from racing you.
A sideboard might help somewhat. Having white lets your board in Stony Silence (for Affinity) and Timely Reinforcements/Kor Firewalker (for Burn). Spellskite is a good thing to have against Burn, Infect, and Twin.
He's asking for advice for porting a deck from one format to another, so I don't see why he wouldn't post the original list.
I can't see why you'd want to do this. Not only is Violent Outburst a terrible card, it reduces the number of cards in the deck that Collected Company can hit, and since the deck is built around Collected Company you'd want to avoid doing that.
If you're willing to splash (which may not be worth it) Serra Avenger is another undercosted beater with a drawback you can ignore. Priest of Urabrask is another ritual creature like BTE (albeit not as flexible). Arbor Elf is probably better than Llanowar Elves since it can untap your Stomping Grounds to get red as well as green. Aether Vial also seems like it would be good here--if you set it to 2, you can get free mana (BTE) or instant-speed uncounterable fatties.
I'd recommend posting this stuff (discussion of sideboard tech and strategy) in the Knights thread since that's where most of the discussion about the archetype takes place--more people will see what you see there.
If you're just looking for a deck that plays Mutavault and Aether Vial I'd look to Merfolk. It's competitive (one of the top ten most prevalent decks in the format, and consistently rated as tier 2) and is likely cheaper than whatever you were looking at since it doesn't play swords.
There is some literature on a less competitive Modern knights deck that plays Aether Vial (link) if you're intent on playing that tribe.
EDIT: The link you just posted seems to be exactly the one in the Knights primer I linked to above. There's tons of info on the archetype there.
Losing out on Boros Charm seems big and I'd look for away to slot it back in. You could probably cut down on the Skullcracks (since Atarka's Command is basically a strictly better version) and maybe one or two Searing Blazes.
I'd highly recommend against cutting any Eidolons. They're extremely powerful against most of the top-tier decks in the meta. You really shouldn't care about how much damage you're taking from them since you'll be dealing more to your opponent.
I didn't catch that you were talking about casting it with Sanguine Bond out--in that case, yes, it does.
I could see a white splash being useful here. It gives access to Path, which is a huge bonus. At that point, though, I'm not sure why you wouldn't just run Rhino and play Junk.
Not sure what you mean by 'scales better'--the cards result in the same gain in life, but Exsanguinate will always cost one mana more. Exsanguinate only scales better in a multiplayer game. I'd argue that Exsanguinate as a single card does more than what this deck tries to grind out with Stream of Life, Sanguine Bond, etc. but the OP seems to be wanting to grind out advantages over the course of the game and removing Sanguine Bond for Exsanguinate makes most of the cards in the deck pretty useless.
OP: If you want to call this thread a primer I'd try to include alternative card choices and a matchup/sideboarding guide at the least. Primers are supposed to be relatively comprehensive introductions to deck archetypes, and this doesn't seem to quite do that at the moment.
This deck seems completely cold to combo. Since you basically have no interaction, you'll be dead when Twin combos out on you on turn four. Since you're running black I'd highly recommend a discard package (some combination of Liliana of the Veil, Thoughtseize, and Inquisition of Kozilek). I'd also cut Doom Blade for better removal--in a format full of Siege Rhinos and Tasigurs, you'll want something that can hit black creatures. I'd recommend Dismember or Go for the Throat. Abrupt Decay also gives you some much-needed interaction against Junk, Twin, and Infect. I'd cut Leaden Myr for Birds of Paradise if you really want to be ramping, but I don't think it's all that necessary since you plan on playing a long game.
Your creature base in general seems a little loose. You're running a lot of indisputably bad creatures just because they gain you life, which really isn't the way to go. Tarmogoyf fits into almost any deck with green and this one is no exception--it protects you and gives you an additional angle to attack from if you can't find Sanguine Bond. If you can't run 'goyfs I'd recommend some number of Scavenging Oozes--not only do they fight opposing Tarmogoyfs, Snapcasters, and Lingering Souls, they synergize with your engine due to the lifegain they provide.
22 lands seems low for a big-mana deck. Nykthos doesn't seem great here--most of your permanents only give you one or two devotion. Additionally, it's legendary and you don't want to be drawing more than one of it. Keeping one or two would probably be okay, but you definitely want a set of Verdant Catacombs in here. Woodland Cemetery couldn't hurt either, especially since you're a two-color deck.
You'll definitely want something like Creeping Corrosion out of the board against Affinity. Choke is excellent against Twin and also hurts Patriot Control and Scapeshift.
The first thing I'd recommend to improve the deck is improving your manabase. Shocks and fetches make for a much smoother and effective curve than taplands.Cruel Control is an established UBR deck that might interest you, and even if it doesn't it'd probably be helpful for you to take a look at its manabase.
This deck also is completely cold to Abrupt Decay and Path to Exile, as other people have mentioned. The issue here is that roughly 30% of decks you'll run into have those cards. Additionally, Remand and Cryptic Command (another ~10% of the meta) ruin your combo and leave you out of gas since you have no way to refill your hand or filter your topdecks.
If you're intent on trying to make this deck works, free Kiln Fiend triggers would speed you up a lot. Mutagenic Growth is excellent for this, and Gitaxian Probe gives free Kiln Fiend triggers and essentially makes your deck 56 cards. I'd also test splashing blue for Nivix Cyclops in place of Foundry Street Denizen. You want to be casting spells in this deck, not playing a lot of creatures, so I think you'd get more value out of Nivix Cyclops. It's essentially a harder-to-remove Kiln Fiend, which couldn't hurt, and splashing a third color in Modern is relatively painless.
I'm not sure how seriously I'd take these analyses, given that all of the test games you've discussed so far have been against tier 2/3 decks. Twin and Scapeshift are the decks you want to be testing against for combo, and you definitely want test against Junk, Bloom Titan, UWR Control, Affinity, and Infect so you have an idea of how the deck fares in the actual metagame. Calling your combo matchup good because you won against a Polymorph deck seems like a bit of a jump to me.
Thank you for the correction! Fixed.
Since Flying Crane Technique untapped player A's creatures, they can block during player C's turn.