Pollution from high protein foods will show itself in the form of higher nitrates (bad for inverts) and the pH dropping to acidic levels as organic acids released from the food break down the calcium buffers that stabilise the waters pH, again very bad for inverts as it softens the shell. To combat this people who keep perdatory fish do regular water changes between 30 and 50% depending on the size or numbers of animals and tank size.
Chicken is fine to feed as an occasional treat but i would offer it no more than once every two weeks. With any animal it is best to try and replicate their wild diet to the best of your ability. Crayfish are aquatic scavengers/predators so put yourself at the bottom of the river where they live and think what you would find there, lots of vegetable matter, small aquatic larvae and other inverts in the substrate (bloodworm, snails, small shrimps etc), the occasional dead fish and very occasionally the carcass of a dead aquatic bird or mammal.