I think they're loud enough to be annoying to a neighbor who already wants to be annoyed. Chances are, any time her dog barks, she'll think it is because of your chickens.
We have four and no one ever notices them, however. Our neighbors even come to visit them! At the last ball game, someone even came and asked if she could take pictures of them running about in our yard.
We have two dogs, our neighbors have two dogs and the people across the street have two dogs. That's a lab mix, beagle, Great Dane, rat terrier, Weimeraner and German shepherd mix who all ignore the chickens completely.
They were all curious at first, especially when we had the run against the fence. But they lost interest quickly. Unless the bird runs, it really isn't that interesting to most dogs. Mine don't. They sit in their tractor and if a dog barks at them, they stand up tall. They've pecked our dogs on the nose, and that killed their curiosity really quickly.
Your neighbor doesn't sound like the most cooperative type, but if she is willing, you could ask for permission to spray it with water. We got a cheap spray bottle of water and trained our dogs to not bark at the neighbors' dog pretty quickly by squirting them in the face when they started.