That is terrible!
I am so sorry for your loss!
It's terrible to be in a situation like that with your neighbor.
Is the neighbor planning to do anything to correct the situation? That's quite a major loss. Chickens are considered livestock and therefor part of your livelihood. There is much discussion about what proper compensation is.
You are gonna get lot's of people feeling rage for you on here.
Some will tell you shoot the dogs. I am an avid dog lover. And I say after a clear warning (not a threat) that the consequences will be grave if they come on your property again... yes I would shoot.
On top of that I would immediately call animal control. They should at least quarantine the dogs while testing for rabies or something and have it documented that the dogs are considered dangerous. What if you got bit when trying to stop the attack? And they were at large while they were roaming your property.
My sister in law is our insurance agent for homeowners' and none of her companies will cover a homeowner who's dogs have killed another animal. They all consider an animal like that to be dangerous. So I was instructed not to tell her if my dogs caught something in our yard, and they have several times including opossum, cats, rats, and gophers.
How is your current relationship with your neighbor? Are their dogs usually contained? How far from you are they?
Your head must be spinning right now.
Hang in there!