Does this book have a happy ending? Why or why not? Explain.

Slaughterhouse Five ends on a surprising note, with a bird tweeting "Poo-tee-weet?" to Billy Pilgrim.
The ending is certainly not a conventionally happy one. The bird tweets a question that humans cannot understand. So, the ending is confusing and perhaps, even a little bit unsettling. This may be the reason Vonnegut ends the story in such a manner. He is essentially reinforcing a main theme in the book: war and the massacre of the living makes as much sense as the tweeting of a bird.
So, from that point of view, the ending of Slaughterhouse-Five is certainly not a happy one. Vonnegut mentions some of the same things in Chapter 10 (the last chapter of the book) as he does in Chapter 1. This would include the "Poo-tee-weet?" bird tweet, readings and memories about the bombing of Dresden, the execution of Edgar Derby (the man who stole a teapot), and interactions with Bernard V. O'Hare (the narrator's war buddy).
Although the references are similar in nature in both chapters, there are slight differences. For example, in Chapter 1, the narrator mentions that he listened while O'Hare read about the Crusades. Also included in the reading was information about the Children's Crusade. The narrator slept in one of the children's bedrooms in O'Hare's house. The text tells us that O'Hare placed a book about the history of Dresden on the bedside table. The narrator relates that he read from the book.
Meanwhile, in Chapter 10, O'Hare has a notebook with him. He looks up the population of Dresden and comes across facts about human mortality rates. It's difficult reading but reinforces the fact that death is very much a part of earthly existence.
Essentially, the references are the same, but the details and events are slightly different. Vonnegut appears to be reinforcing the Tralfamadorian point that "all moments, past, present, and future, always have existed, always will exist." So, each moment exists permanently. Vonnegut seems to be making the point that the Tralfamadorian sense of time is like war, which will never be eradicated as long as time shall last. And certainly, that is not a very happy conclusion to a book!