Any dog could kill your chickens. Will they depends on a lot of things.
Our neighbors have two blues who are very well trained. When we first put the chickens and rabbits in the outdoor pen, we brought the dogs over and had them "meet" the animals. We reinforce often that the dogs are not to chase the birds and bunnies. We praise the dogs often and offer biscuits when they obey. The chickens come out of the pen for daily free-ranging; the dogs are curious but so far haven't shown any desire to chase them. The chickens and rabbits are tolerant of the dogs' presence but I certainly wouldn't say they are comfortable with the dogs' presence; they keep their distance.
These same dogs have a blood lust for squirrels, moles, snakes, toads, and scorpions and kill plenty of those around the yard. They chase deer but leave the cows alone. They chase coyotes and raccoons but are friendly to other dogs. They bark at adults but love kids. I am thankful for the dogs as they keep predators away from my animals.
Having said all that, I would still be wary. You never know when a dog will have an "off" day.
At the very least, you could make friends with your neighbor's dogs, get them to listen to basic commands, such as "STOP", "SIT", and "NO". Introduce them to your birds. Be sure they know certain areas of your yard are off limits. Offer tasty biscuits and plenty of praise when the dogs do visit. And voice your concerns to your neighbor; you both can work together to keep the dogs on thier best behavior.
Good luck!