Billy's dead

Billy's time in the war and his subsequent trauma lead him to come to two conclusion that pertain to your question. One, that time, as the Tralfamadorians say, is non-linear. For humans, time passes, and people, events, and phenomena in general come to an end once their time is complete. This is the nature of time. For Tralfamadorians, however, a person may live and die, but will always have existed at some point, and since time is non-linear, they always will be in a constant state of existence. It's basically like real-time memory. This is one of the main reasons that Billy views his imminent death as rather inconsequential. If he lived once, he always will be alive, in some way or another. The second reason that Billy is so calm about his death is that he subscribes to a fatalistic ideology. He believes that everything that happens must happen, because it is pre-ordained. Thus, he views his impending demise as unavoidable, and simply accepts that it must happen. This acceptance comes back to his view that time is non-linear. Essentially, Billy sees his death as both necessary and irrelevant to the bigger picture of life.