In our neighborhood, we also have our own "hound from hell" who finds great delight in calling in complaints on all the neighbors.
It was his dog that killed my goose a few days ago. His dog climbed over the fence.
I think it's important not to retaliate, get vindictive, or provocative towards people who behave like that.
Your neighbor could be afraid of your birds. When I spoke with our own "hound", I discovered he was terrified of birds. He knew someone who died from a bird disease.
He was pleased with the way I was taking care of my flock, and the extra mile I go to ensure their health. And I assured him that if he ever had a question or concern, to let me know and I'd be happy to resolve it. He was very surprised that I knew so much about bird diseases.
Here in my City, we can't have roosters. Roosters don't bother me, but they do some people. Aside from the crowing, roosters can be dangerous. That is a concern of mine since I do have children here quite a bit.
I'd sure talk to the guy if it were me.
Ya might be missin out on somethin special -- like a new friend!