Punishment will decrease the incidence of the behaviour that immediately preceded it, reinforcement will increase the behaviour that preceded it. From what I understand from veterinary animal behaviouralists and certified pet dog trainers, for positive reinforcement or punishment to work, they must be immediate. Human beings can remember the past, link together unconnected events and have remorse, dogs do not.
Here's what worked for me - it takes alot of work and time. I have 2 dogs, a pitt / lab mix who is very prey driven and a sight hound. It starts with lots of exposure to the chicks in a totally controlled environment in which they cannot fail. Dog is on leash to start and not close enough to chicken to bite. If they did anything bad such as lunging toward, or opening mouth to the chicken, they were corrected immediately - the response is measured, for one dog it only took a minor correction, for the other a pretty strong correction. However using only punishment can lead to resentment and fear and
doesn't really teach what you want them to do. Positive reinforcement does and animals respond well to it, so also be sure to reward good behaviour. Dog looks away from chicks, praise and treat. Dog relaxes and stops fixating on chicks, praise or treat. Eventually when dog can be trusted, dog can sniff chicks (monitor very carefully in case dog is not ready). If good, be positive! If bad, be negative. We spent hours hanging out with the dogs and the chicks. Eventually - and it takes lots of repetition - you get to the point where you are rewarding the dog for good behaviour around the the chickens and rarely have to use any discipline. Our prey driven dog really loves to play fetch, so we can also use this distration to our advantage, and play fetch instead of fixating on chickens. This overall approach works with dogs whose desire to please you and do what you want outweighs their prey drive. For some, I imagine it may be impossible no matter what you do.
I can now trust my dogs off leash in the proximity of the chickens. If this doesn't work with your dogs, you'll know and can keep them separated. But do give them a chance in a safe environment, it can work with some of the tough ones. I hope this helps.