Sorry for the loss of the chicken, but we do things a bit different. For a dog, we do part ways in a similar manor. Say some words, put a favorite toy with them, and bury them. With livestock, it is a completely different thing. Won't go into details but we just believe that food is food, and companions are companions. Children are exposed to false reality everyday, and sometimes get angry when it hits them in the face. If your son gets angry, I would get angry back. Let him know that life is not all puppy dog tails and butterfly wings. Death and tragedy happen and the sooner he learns to deal with it the better.
May sound tough, and I mean ABSOLUTELY no disrespect, and do not mean to sound as if I am pointing my finger or anything. Just how we handle life and death out here. Our kids are NOT the center of the universe, just a very small part of it. Perspective I guess.
I would put the chicken in the coop, and make him get it out, dig the hole, and fill it. Guardianship has responsibility.
This is strictly our opinion though, I would not ever assume you are not doing a decent job raising your children, and would NEVER assume I could do a better job of it. Along the same lines, our method of handling the same situation could be 100% wrong as well.
God Bless