If the target creature is an illegal target by the time Fists of Flame tries to resolve, the spell doesn't resolve. You won't draw a card.

The bonus that the target creature receives is locked in as Fists of Flame resolves, counting the card drawn during its first effect. The creature won't get an additional +1/+0 if you draw another card later in the turn.

If a spell or ability causes you to put cards into your hand without specifically using the word "draw," Fists of Flame's effect doesn't count them.