This was an issue that was reported and then reported fixed, but still is a persistant problem.

Chickens in a chicken cooker who are killed by a lava block, do not burn. This means the chicken will be killed by the lava, but not cooked.

This is similar to hostile mobs not burning when standing on slabs, as the chicken cooker requires the adult chicken be standing on a slab when it's head is in the lava.