Why does Bud keep the Dusky Devastators of the Depression poster?

The answer to this question can be found in chapter 1 of the book. Bud is telling readers what is in his suitcase, and he tells us about a flyer that has a picture of Herman E. Calloway and the Dusky Devastators. It's a flyer that is advertising an engagement that the band will be playing for. Bud keeps the poster for two reasons. One reason is that he knows the poster is somehow important to his mother.

I remember Momma bringing this flyer with her when she came from working one day, I remember because she got very upset when she put it on the supper table and kept looking at it and picking it up and putting it back and moving it around.

Bud isn't sure why the flyer or similar ones are important to his mother. She dies before he has a chance to ask her. All Bud knows is that if the flyers are important to his mother, they are important to him. The second reason that Bud keeps the flyer is because it has a picture of Herman Calloway on it. Bud believes that Calloway is his father. He believes this because of how his mom reacts to the posters, but Bud also sees himself as similar to Calloway. It turns out that there is a good reason as to why the two characters look similar. Calloway is Bud's grandfather.