My chickens go nuts over our dog's food. We once put it inside her kennel close to fencing and they stuck their heads through the fence to get at it.
I think it would be wonderful for you to put out chicken feed and I'm sure they'd eat it too, but I don't think that would be a guarantee that they'd leave the cat food alone, if they have a taste for it. Actually, I'm kind of surprised they'd eat alongside the cats. Cats prey on chickens. Maybe they are really hungry, and would gladly eat somewhere else if there was food for them.
Despite what people think, chickens aren't herbivores. They eat insects and small mammals and amphibians (I've witnessed this--practically gave me nightmares).