Excellent question. I would add to the previous post that the sequence in which the texts are written do not necessarily represent the sequence of fictional events. In order to figure out what is going on and who lives and dies in what narrative, consult a genealogy chart ( see the link below). Faulkner is notorious for either resurecting characters or telling stories through charcters that are already dead like in Absalom,Absalom! for instance. To pinpoint who dies when, you have to go into the specific narratives.
I believe that Sarty's father, Ab does die in the story "Barn Burning" but not from the gunshots. I think what is confusing you is there was a trilogy written by Faulkner after the book "Barn Burning" which does talk about Ab and his life. The trilogy is known as the "Snopes Trilogy" - "The Hamlet", "The Town", and "The Mansion". Actually "Barn Burning" shows was happens to Ab in the future. So you are seeing the end of Ab's life in the "Barn Burning" and then go back in time in the Trilogy. Hope this helps answer your question. Remember, I believe he dies in the end, but not from the gunshots because Faulkner refers to this in his future writings.