My understanding is "no" that worms from dogs to chickens, and chickens to cats, visa-versa, etc... my understanding is that is not an issue. At least not from the poop... My chickens eat dog poop, my dog ate the chicken poop. It would/might be an issue if the cat killed and ate a chicken with worms? Or, if the chickens killed and ate the cat?? My understanding is the worms need a live host. So... a bug eats the fresh, very fresh poop, worm eggs, etc.... the bug carries the worms, the chicken eats the bug... the chicken has worms, caught them from the insect. Cats get worms from killing and eating live things, mice, birds, etc. Not sure if I am relaying that all correctly. Also, the tapeworms that dogs and cats get are a different variety from what chickens get? From what I have read? And, tapeworm segments do not survive long outside the host... so... if they are expelled in the poop of a cat.... or dog, and a few minutes, a day, a week later the chicken eats the poop, the tapeworm segments / eggs are dead, not viable.
I am sure someone else can better explain it. It's still good to worm everyone, cats, dogs, and chickens now and then.