Oh, the little chickens seems to stop flapping their wings, riding a Entity, on a Lead, or in Water, pretty much anything that makes them flap like a madman. (Just to let you know, I was using a texture pack, but it won't effect the bug)

The gamemodes were SP, S, and C, because I was messing around with redstone, and getting stuck in it.

To reproduce:
1. Spawn chicken, on lead, hanging, riding a Entity, or Swimming in water.
2. Chunk load for 1 HR, if not, longer (Reason: If not chunk loaded, the chicken will be flapping their wings, still, once you get back!)
Now you got your self a non-flap chicken.

Want to see, check 2014-09-22_23.11.54.png
(Been edited, to make more sense.