We raise show dogs that eat chicken poop all the time since our flock free ranges. BUT I give the dogs Ivermectin every month to control the paraisite situation. Dogs dont win ribbons with wormy bellies and dull coats!Eating chicken poop won't hurt them in a grand illness, life threatening way. Some dogs just have sensitive tummies. Mine do not get sick from it but Mega's dog seems to be which isn't really surprising. In general it's best not to eat poo. There is a small possibility that a dog could contract a parasite but its small and only if they chicken is very infested. Just something to be aware of. All of this is treatable.
My chickens free range in my yard so I end up with little chickens poos all over the place and if left to their own choices my dogs would search the yard and find them all and snack it up. I try to discourage this behavior. I have trained them to stay out the coop (which I leave open when the hens are free ranging) and they are good about that but they do pick up the poo out in the yard. I don't really worry that much about it, I mostly just think its kind of gross.