Don't know if spraying it directly on the chicken would be good. Might be safe but don't know exactly. I would be hesitant. Maybe use neem in coop and the ivermectin on the chicken. I've never had to deal with mites yet ( thankfully sure my day will come ) but heard its best to treat the coop...
I use it for my garden it helps with a lot of different types of bugs. Which I guess you've noticed. If you don't spray it in the nest boxes and maybe spray the rest when the chickens are out giving it time to dry I would think it would be fine assuming diluted