You've created a problem here. Personally, I would start very very slow. Like Doc E is asking how birdy is your dog? If he's already been fed treats, I don't think treats are going do it. Birds are quite different than treats. Treats are treats, but with birds you are working with the dog's natural instinct.
I would start with a cheap cap pistol from a toy store. Something that's not very loud. Go to a gamefarm and buy a dozen birds. Tie the legs w/ chord on the first one and tease the dog. Get the dog so hyped up that the sound would be un-noticed. If the sound still bothers the dog, put the gun away till another time.
You can also use a pigeon with primary wing feathers pulled so it can't fly but the method is the same. Do it till the dog ignores the sound. Then graduate the sound. Someone to help in shooting will also help alot.
I would use: cap gun->starters pistol w/.22 shorts (or something like popper rounds)->.410ga primers ->.410ga ->20ga or 12ga. It may be overkill but the dog is already showing signs of gunshyness if not already gunshy. So, you have to start real slow.
Good Luck