I can't find anywhere that says Snatch is an egg move for Fletchling, everything in the Flying egg group that gets it learns it from the B2W2 tutor, and Pokebank is obviously not out yet. You may want to replace Snatch with a TM move on your Fletchling.
Hey Mate!! Just wanted to let you know that it looks like both you and gem accepted my challenge?? (she accepted a few posts up but didn't update the queue) So if you wanna battle still then we should totally do that, just we need a ref uvu (I'll make a post in the battle tower about it if you're cool with it)