If you control more than one Shrieking Affliction, the ability of each one will trigger separately, as appropriate (C.R. 113.2c). Note, however, that the ability has an intervening "if" clause, which checks whether the opponent it refers to "has one or fewer cards in hand"—
at the moment it would trigger (if not, the ability doesn't trigger) (C.R. 603.4), and
at the moment it would resolve (if not, the ability does nothing) (C.R. 608.2a).
Dose Shrieking Affliction's effect happen twice if I have 2 on the battlefield?