So how with all of my dogs I've worked exclusively with them first. I teach them recall, sit and stay, etc. A big thing is desensitizing, as a lot of dogs won't jump or chase until something else starts panicking around them. At this point I take them outside, preferably to parks or other places with many other birds, squirells, etc. When they walk calmly and look at you, reaard them. If they jump or bark, or show alert at all towards any kind of small animal that is not showing aggression first, do not reward them. A sharp noise or correction until they look back at you can do good, then rewards them when their attention is back on you. I then practice bringing my dogs on walks near the chickens with the same corrective technic. This may have to be practiced for a while until the dog shows absolutely no interest in the chickens when passing. Then this can be practiced on a leash while chickens are out. If the dog perks its ears or shows any kind of prey-intent on the chickens, correct and get attention on you again.
This works faster and better on eager to please dogs, and may take longer on extremely prey driven dogs. On the latter, one must have lots of love and patience for their dog, but if given the right training and love you will notice it works wonderfully. Also, it really helps when you give the dog discipline training before starting desensitizing, as it will make them more eager to please and easier to control.
I have three dogs. One was born here, one was a puppy when we got her, and one was a year old hyperactive rescue when we got him. While I wouldn't trust them alone for long unsupervised periods of time with other prey animals (as should be the case with ANY predator, no matter how well trained its almost impossible to know all of their triggers and be able to avoid them) I would trust them off leash with the chickens free ranging. If I see something happen that might trigger their instincts, I am simply able to recall and keep their attention until it passes. Another quick note, if the dog pulls on the leash, bring them inside or away from all other distractions immediately. This teaches them they won't even be allowed to see until they calm down. This usually works wonders as dogs are very curious and will do what it takes to see what they want to see.
At one point I raised pygmy goats, and some evil person snuck onto my property while I was put of town and shot all of them. All died except one, which is when I assume they ran out of bullets. My goat had a bullet hole in his face but was otherwise fine. This was when the person went into my home, put my wounded goat in a smaller pen, and forced my three dogs that were much larger than him to go into the pen to finish him off. This goat was smaller and had fresh blood scent on them, but my dogs did not touch him. He survived and is now living on a rescue. A bonus note, my dogs have never jumped at or shown attention at my birds, asides from the first time they met when they were promptly corrected and haven't done again since.
You most likely have already found the solution to your problem, but I hope this helps in the future and helps others with similar problems.