If you can read this dude's name without snickering, you're way ahead of us. Kilgore. Trout. This character must have been mocked so hard in middle school.
Kilgore Trout is a (fictional) science fiction author whose stories bear a significant resemblance to Billy's descriptions of Tralfamadore. Trout writes many, many books, but no one besides Billy and Eliot Rosewater, another veteran, have ever heard of him. The thing is, he has great ideas, but he's a terrible writer.
The most important thing about Trout is that he imagines the world operating by new and different rules, in ways that Billy finds comforting and necessary after being so disappointed by reality during the war.
Trout lives in Billy's hometown and the two become acquainted. When we actually meet Trout as a character we find that he is socially maladjusted and sadistic. At the same time, he has greater insight into Billy than any of the other characters. When Billy has a flashback to the aftermath of Dresden while watching a barbershop perform at his anniversary party, it is Trout who suggests that Billy has seen through a time window (8.16.4). Given that Billy sees himself as a time-traveler, this is pretty perceptive... but it is also an imaginative way of describing a flashback, a moment when you are suddenly looking back at a terrible event from your own past.
Maybe Trout is yet another stand-in for Vonnegut himself: after all, Trout is a writer, and he does invent a lot of the concepts that come up in the novel. What's more, Vonnegut also reinvents the universe to fit new rules—Slaughterhouse-Five and many of his other novels fit into the category of science fiction. Which would make Rosewater's comment that Trout has great ideas but is a terrible writer kind of an in-joke or self-jab on Vonnegut's part.
Dude writes a lot. Let's take a look-see into his canon.
(1) Maniacs in the Fourth Dimension (Chapter 5, Section 25)
Kilgore Trout claims that there really are vampires and werewolves, heaven and hell, but we just can't see them... since they're in the fourth dimension. Oh, okay.
(2) The Gospel of Outer Space (Chapter 5, Section 30)
The hero of this novel is an alien (who looks like a Tralfamadorian) who wants to know how Christians can be so cruel. The alien decides that the problem is the New Testament, which is supposed to teach people to be merciful but actually seems to teach them that "Before you kill somebody, make absolutely sure he isn't well connected" (5.30.7). The problem is that the man the Romans crucify is already the son of God, so of course everyone's going to think it's wrong to kill him.
If Christ were just a nobody, would it have been any more okay to kill him? The alien decides it would be better if Christ were not actually the son of God, but still said all the same stuff. Then God could come down just before Christ dies on the cross to say that he is adopting Christ, and that from that day on, it is wrong to persecute anyone who is "a bum who has no connections" (5.32.3).
(3) The money tree (Chapter 8, Section 7)
Trout describes a money tree with 20-dollar bills for leaves that attracts people to it so they will kill each other around the tree's base and become its fertilizer.
(4) The Gutless Wonder (Chapter 8, Section 8)
Even though this book is written long before World War II, it still predicts the dropping of jellied petroleum devices to cause firestorms. The person who drops these special bombs is actually a robot. He is shunned by society not because he is a mass murderer, but because he has bad breath. Once he fixes his breath, everyone welcomes him.
(5) The mysterious zoo novel (Chapter 9, Section 26)
This novel is sitting in the porn shop where Billy sees the film of Montana Wildhack before going on the radio to talk about Tralfamadore. The novel is about a man and a woman from Earth who are kidnapped by aliens and put in a zoo.
(6) The mysterious Jesus time-traveling novel (Chapter 9, Section 28)
This is another porn shop Kilgore Trout novel. The hero travels back in time to find out whether Jesus really died on the cross, or if he was taken down before his death, thus explaining the "Resurrection." The time-traveler arrives before Jesus has discovered that he is the son of God, while he is still working as a carpenter for Joseph, and Jesus builds an execution device at the order of the Romans. But then Jesus himself is crucified and the time-traveler finds out that his heart has really stopped beating: he is absolutely dead.
(7) The Big Board (Chapter 10, Section 3)
The narrator seems to imply that Trout gets the idea for this novel from Billy, who says that the Tralfamadorians really like Charles Darwin. Darwin tells us that the death of the weakest improves the species. Trout uses this idea in The Big Board, in which aliens ask the hero about Darwin and golf. (Sound familiar? It's the same as the mysterious zoo novel... or so the text seems to imply.)
When you look at all of Trout's works together like this, you can see a lot of the elements of Billy's own life story in them: the Tralfamadorians in The Gospel of Outer Space; the ethical and religious issues in The Gospel of Outer Space, The Gutless Wonder, and the time-traveling novel of Chapter 8; the alien zoo in the mysterious zoo novel of Chapter 8; and the fourth dimension in Maniacs in the Fourth Dimension.
This makes us wonder, once again, if Billy is meant to be crazy in the novel—or whether it even matters. After all, Billy and Trout are both fictional creations of Kurt Vonnegut, so who cares which of them gives ideas to the other? Neither of them is real. Whoa, our heads are spinning.