You smacked your dog's head and backside for THROWING UP???
I'm sorry about your dog, but please do not get another if that is your response to a dog getting sick.
If you think that your smacking his head could have caused his death, then you basically severly abused him, since you would have to really hit a dog's head with some force to do that kind of damage.
Most likely, the chicken bone punctured something and he bled out internally.
If you care about dogs, then read about positive reinforcement training, and vow never to smack or hit a dog again. There is no reason to, and I am speechless, that you would do it in response to a dog getting sick.