I would assume you can't have farm cats and chickens at the same time? (Unless the chickens are housed safely away from the cats?)
I've only had a couple of cats over the years that weren't chicken compatable. Those cats got culled from the rest pretty fast.
The chickens have a coop and run seperate from the horses. I do occasionally let the chickens out to scratch around the manure pile. The horses mostly ignore them.
My dogs are chicken killers so that's who I have to keep very seperate from each other.