If the chickens are living in a secure pen, that predators cannot access, dyeing would make no difference at all....and then be made easier predator targets...
If the chickens are exposed to predators, dyeing could change things, but it would probably depend on what color the chicken is. A white chicken might be even more obvious than a dyed one.
(I'm not really in favor of dyeing chickens, but I don't think it will make a very big difference to the risk of being eaten by a predator.)