Even if you section off an area for your chickens/dog, you still need to spend a lot of time socializing/training your dog around your chickens, because there's always a chance that the two would meet accidentally.
There's no magic button. It takes weeks and weeks of you diligently working with your dog around your chickens. Does he respect you as pack leader; you mentioned he often doesn't listen to you on commands...in your opinion, is that because he wasn't really taught, or because he doesn't see you as the leader??? If he doesn't see you as leader, then honestly, the dog will probably never be okay around chickens.
If he does see you as leader, then he may be trainable.
For two weeks, sit with him HOLDING HIS COLLAR right there among the chickens. Within a few days, sprinkle treats around the two of you, so that the chickens come near. Have a command word ready, such as "nice" or "gentle" (only choose and use one word). If he's treat motivated, praise him and give occasional treats while he's sitting or laying there nicely.
After he's doing well with that (don't rush it), go for a week or two doing the same thing, but with him on a leash instead of hand-on-collar. Keep the leash short if he's iffy, and keep your eye on him the whole time.
If he does well with that, then go to walking around with him on leash, around/among the chickens, always using your command word and giving treats for postive responses. Once again, I would do this daily (several times a day) for a week or two, depending on whether he's complying.
Finally, progress to walking around with him off leash, using the same techniques.
Even if he's able to make it through all of these steps, I would not allow him with your chickens alone. I would sit somewhere and watch (but don't show that you're watching.
Dogs are only as consistent as we are as trainers.
And depending on what he's mixed with (labs are typically very easy to train, but the other mixes???), his prey drive may just be too high. Or if he doesn't see you as the alpha, then it probably wouldn't work either. But it's still good socialization for him, and important that he see your chickens as part of the pack, rather than something to be hunted, and it will most likely lessen the chance of another kill... good luck!