Conflict is the driving force behind any good story, so if "The Ransom of Red Chief" didn't have conflict, it wouldn't be a very good story at all. In this story, the main conflict comes from the little Johnny that Bill and Sam kidnap. He turns out to be much more of a hassle than they had anticipated. So, what was supposed to be a quick, easy, standard kidnap and ransom situation, turned into pure torture as Johnny, or "Red Chief" torments and humiliates Bill. Bill is forced to be Johnny's playmate, which means being a victim in all sorts of pretend games. For a grown man, this is completely embarrassing, and painful in many ways. The kid is a handful, a bully, highly annoying, and full of never-ending energy. He creates the conflict because Bill wants to cut the entire scheme off just to get rid of the kid, whereas Sam wants to follow through on it, so begs Bill to hang in there a bit longer. The conflict in the story helps us to see Bill develop from a strong, assured, confident criminal to a dejected, broken, humiliated play-toy of a little boy. His pride is trampled on, and he hates it.
I hope that those thoughts get you started; if you haven't read the story yet, I highly recommend it. It is hilarious, and an easy read. I provided a link below to further commentary and analysis that will be useful also. Good luck!