If the chickens were killed on his property, you are liable. If they were killed on your property, you might not be. I say might because a few jurisdictions have arcane laws about right away for roaming livestock (those jurisdictions are rare). If the birds were purebred quality stock, $15 per bird probably won't cut it. If he wants adult birds, he may have to purchase them online or from local sources. If the birds have to be shipped to him, that can be expensive. At this point, it is normally the injured party that establishes the value. At that that point, you can either pay or dispute it. Even if you locate replacement birds, he can claim that they are inadequate due to age, breeding, color, conformation to APA standards, etc. I'm glad that you are trying to make this right. I had to take a dog owner to court recently. BTW, 13 birds ended up costing him over $1000 plus court costs plus lawyer fees plus my legal fees. All that on top of the fine. He would have been much better off just paying for the birds.
I strongly recommend that you contact the chicken owner and ask him what he feels is a reasonable replacement cost. Only he knows the costs that he has in them, the age, breeding, etc. If he had quality show birds and the dog decimated his breeding stock it is a lot more expensive than if he had birds from commercial hatchery stock. If you are afraid that a personal conversation will be hostile, put it in writing and mail it to him.
Also, please have your wife take the dog through obedience training. A well trained dog is a blessing and a joy. A large unruley dog is not. I can tell you from personal experience that having a dog decimate pets that you raised from babies is heartbreaking. There can be a lot of time, blood, sweat and tears getting a flock to laying age. Yes, they can be beloved pets. The dog now knows where the chickens live and how much fun they are to kill. Without adequate training and restraining measures, it is only a matter of time before he does it again.
Also, I would like to thank you for taking responsibility and especially for not saying, "they were just chickens."