We asked for 6" coverage but the bobcat wasn't very precise, so some areas got more than 6", and some got less. I'm not sure about the chicken area. It will definitely be several inches of clean soil plus several inches of wood chips on top of that. I'll watch out for excessive digging and put down rocks or pavers as necessary. It's the best I can do.
You should be okay with that depth. My chickens haven't dug that deep.