I have always let my dogs and chickens out together. Even my Shiba couldn't care less about them and would rather eat their poop. They have all been told not to bother them with the "leave it" command. If your dogs are 100% solid on this command, they should respect it.
Bird dogs are not used to kill birds, they will watch and wait until given the command to retrieve a dead one, and then they do so while being as gentle as possible. They tend to view birds as toys instead of food, and can be trained to ignore them when they are alive (so they aren't caught between a bird and a gun) and "fetch" dead ones for a reward. Poodles are retrievers, not hunters. Breeds that are more likely to kill birds are Akitas, terriers, huskies, and sight hounds. I wouldn't trust a Fox Terrier or Airedale, but poodles, doodles, spaniels, and retrievers are as safe as you can get because for the most part we have bred true prey drive out of them.