The flyer, along with the suitcase, is a very important possession to Buddy, as he thinks that in it somehow lies a clue to the identity of his father. In the first chapter he tells the reader how he remembers his mother getting very upset one night as she constantly looks at the flyer and then puts it back down, and ever since then he has treasured this flyer, which advertises a jazz band, as a symbol of the hope that he has that he might be able to connect with his father at some point in the future. Note what Bud himself says about the flyer:
The paper was starting to wear out from me looking at it so much but I liked checking to see if there was anything I hadn't noticed before. It was like something was telling me there was a message for me on this flyer but I didn't have the decoder ring to read what it was.
Bud's feelings about the flyer are therefore particularly important. He treats it as if it were some kind of puzzle that he tries desperately to work out, because if he can, the flyer will hold the secret to his father's identity and location. From the way that Buddy himself admits that the flyer is now "starting to wear" because he looks at it so often, the reader can see how desperately Buddy desires to find his father. The flyer therefore symbolises his hope of meeting his father some day.