Rather than employing a conventional third-person ‘‘narrative voice,’’ the novel is narrated by the author himself. (eNotes)

The novel is narrated by "Kurt Vonnegut". We will put his name in quotes here because the narrating voice is identified with Vonnegut as the author but also is associated with Vonnegut as a character in the story. 

The narrator speaks directly to the reader through the first chapter then tells the story of Billy Pilgrim. During Billy's story, the narrator inserts references to himself as a figure in the war on at least two occasions.  

There is only one speaker then, but this speaker switches from first person narration to third person narration when he begins to tell Billy's story. This method of narration is unorthodox and serves to complicate the text in ways that support the themes of 1) the importance of perspective and 2) story-telling, not as re-telling, but as a creative act. 

Who is the speaker in Slaughterhouse-Five, and how does the speaker change?

In Kurt Vonnegut's Slaughterhouse-Five the speaker is Billy Pilgrim. Pilgrim is a man who has become unstuck in time. He simultaneously is experiencing his life as a prisoner of war in WW II, a married businessman much after the war, and a prisoner on the planet Tralfamadore. The plot focuses on how Pilgrim copes with his life. The story is a satire and is based loosely on Vonngegut's own experiences during the bombing of Dresden during WW II. To say that Pilgrim changes is true, but he does not change in the same way that a person who is living a linear life would change. He is changing constantly and hoding all of those changes simultaneously inside himself. He can see what he had done, what he is doing, and what he will do. Essentially, he remains the same person while things change around him. It gives him a greater perspective on life and death than he would have if he had not been abducted by aliens and put on display for their entertainment.