The sign for chicken looks a lot like a beak pecking the ground or scratching for food. To sign chicken, start with the bird sign. Take your thumb and index finger and make an open beak, while making the rest of your hand into a fist. Close the beak and bring it down to peck at the ground as represented by your other outstretched hand, palm facing up.
We use chicken for the animal and not for the food. One of our favorite story books has a chicken. "Look, it's Chicken Little!"
Cluck, cluck, cluck! You can add a lot of interest to the animal flash cards by doing a little bit of animal onomatopoeia. The sounds add a lot of interest for babies and makes it a bit more fun.