How to Free Range Chickens?
If you don't have a fence to keep the neighbor dogs out, I wouldn't risk it. Your own dogs, you can put them up for an hour while the chickens play outside. You don't have that option with the neighbor dogs unless you call over there and ask if they wouldn't mind keeping them up for a little bit.
We split our yard 3 times.. an area for the chickens, one for the dogs up by the house, and a larger "open" area with the firepit and what not where either the dogs or the chickens can play, or neither of them if we have company. The chickens and ducks beg worse than the dogs do when food is around. At least the ducks are polite, they'll stand at your feet and look at you. The chickens, a couple of them will come into your lap after whatever you have. LOL
We like fences. My dogs are cool with the ducks, the chickens too if I'm out there. Sometimes we have everyone out hanging around. Sometimes the chickens are in a mood and flutter around too much, which stresses the girl dog out.
There is a terrier mix that runs across 3 yards to get to our fence and look in, one spot in the fence where it might be able to gain access. So I never leave the birds out alone. They get let out during yard chores and coop chores.
I've lost one duck to a hawk when I popped in the door to change laundry. Won't do that again!
- Anachronistic Anomaly
I wouldn't mix your dogs and your chickens if you have any doubt about what your dogs may do. Either keep your dogs inside the house, a garage, or in a run when you free range the chickens or don't free range them.
If your neighbor's dogs run loose and can get onto your property and after your chickens, then you either need to talk with your neighbor about securing their dogs or risk losing birds.
Ultimately, I wouldn't let your birds free range at all unless you have the time/ability to be out there and with them the whole time they're out...just in case a dog (or any other predator for that matter) shows up. If you've got a roo, then (assuming he does his job) you've got a warning system in place, but a roo isn't likely to stop a large dog.