If the targeted creature is an illegal target by the time Flesh Allergy resolves, the spell doesn't resolve. No player will lose life.

You can target a creature you control, then sacrifice that creature to pay the additional cost. However, if you do, Flesh Allergy won't resolve for having an illegal target. You won't lose any life.

Flesh Allergy counts each creature put into a graveyard from the battlefield that turn, including token creatures, the creature sacrificed to cast the spell, and the targeted creature (if it is destroyed).

You must sacrifice exactly one creature to cast this spell; you cannot cast it without sacrificing a creature, and you cannot sacrifice additional creatures.

Players can only respond once this spell has been cast and all its costs have been paid. No one can try to destroy the creature you sacrificed to prevent you from casting this spell.

If Flesh Allergy resolves but the targeted creature is not destroyed (because it has indestructible or enchanted by an Aura with umbra armor, for example), its controller will still lose life.