It sounds as if perhaps none of your dogs has a killer instinct with your birds, which is good. It just takes work and time. Do your dogs know the "Leave it!" command?? That would help tremendously.
I taught my dogs by taking them individually into the chicken run (on leash, with my hand on the collar initially). I'd sit down, and make the dog sit down beside me. I'd lure the chickens over with treats and let them mill around me and the dog. My command was "Easy" or "Gentle" (with diff. dogs). After a week of that, I progressed to doing the exact same thing, but with hand off the collar - loose leash. Then to walking around the run w/the dog, loose leash. Then walking around in the run with the dog off leash. Then finally to walking around with the dog outside of the run with the chickens. My whole process lasted over a month, and even after that I would "hide" and monitor, because some dogs will act differently when they know they're being watched by their humans.
Of course now my chickens and dogs are both out and about our yard with no issues. I do have people-pleaser breeds though, so that makes some difference I'm sure.