Breakfast of Champions is a book about two men - a used car salesman in Indiana who is slowly going insane and an author, Kilgore Trout, who is ultimate the cause of the salesman's final psychotic break. The two stories run parallel as they move towards an inevitable conclusion. Although the true ending is one that's difficult to see coming.
In this book, Vonnegut represents the time (1973) and clearly uses harsh language - both directly (he seems more free to use profanity than any time before) as well as through controversial topics of race and sex. Clearly the book is meant to upset people, something indicative of the time period in culture. In fact the character of Trout has pretty much made it his life's mission to use his life to make others uncomfortable. Vonnegut clearly wants us in upheaval.
This is not a book for Vonnegut novices. He includes a lot of characters and speaks about his own writing in a very meta sense - even including himself as the author as a character in the book interacting with the characters he creates and including other books even though they don't take place in the same literary universe. It can be a bit confusing for those without the background in Vonnegut's work.
He also seems to release this early group of characters, spanning nearly 25 years of his life. He seems to end a cycle he began in 1950 - as an attempt to deal with his experiences in WWII and finding a way to communicate his thoughts to an audience. Slaughterhouse Five is the pinnacle of that cycle and Breakfast of Champions is sort of an epilogue.
I don't recall if he really has ended his relationship with these characters (I'm re-reading the books in chronological order), but clearly his life and career took a turn at this point. He became both insanely famous and, in a sense, more complete. He had found his second wife and achieved a level of contentment that allowed him to becomes the sage we knew for the last half of his life.
This book is more important for what it represents in the life of one of America's greatest writers than anything it includes in terms of plot or literary value.