It sounds like Jack didn't want to kill them or they would all be dead. I have two boxers and a new Jack Russell and the one boxer LOVES chickens... the only thing is the chickens do not like to play with dogs. Most recently, I go out to find that the boxer, Heidi, got out again and the bantam flock was having a fit, so I go to the birds first. One of the bantam cochins were in with standards (BR, Dels, and SL Wyandotte) and was getting the crud beat out of it, so I saved him. As I was walking him over to the bantams flock, my little Japanese comes around from the back... SOAKING WET... she was being washed by my boxer for God knows how long. Heidi comes out smiling and following the Japanese around like they were now best friends. GEESH!
I guess my point is, I think Jack doesn't want to kill them... maybe just played to hard with the one. So, it really doesn't matter if he sees them as your pets or his food if he still is going to play rough with them. I think you need to teach him that they are not toys. I know its hard depending on the breed and the temperment of the individual dog, but now Jack has seen how much fun they can be flying about and making all those fun noises. You just have to teach that they are not toys, just like you taught that furniture was not a toy.
Good luck... it takes time, patience, and understanding. Glad you only lost one and the rest come back. Chickens are really good at hiding.