I would want to argue that the major conflict we see in this story is an internal conflict based in the character of Kenny, our narrator, who we gradually see being forced to grow up through the experiences that he has, especially when he and his family go to Birmingham and experience a violent racial attack. This initially greatly shocks Kenny, and even when he and his family return to his home it is clear it has greatly impacted him, making him withdrawn and isolated from others. However, what resolves this internal conflict which features Kenny's inability to accept and process what happens is the conversation that he has with Byron regarding fairness and justice. Note what Byron says to him:
"Kenny, things ain't ever going to be fair. How's it fair that two grown men could hate Negreos so much that they'd kill some kids just to stop them from going to school? How's it fair that even though the cops down there might know who did it nothing will probably ever happen to those men? It ain't. But you just gotta understand that that's the way it is and keep on steppin'."
Kenny thus realises that unfairness is a part of life, and our only response to this central truth is to accept it and not to let it interfere in our own lives as much as possible. We cannnot allow the unfairness of life to result in our own inaction and detachment from it. The only response, as Byron says, is to "keep on steppin'" regardless. Thus we see that by the end of the novel this central internal conflict within Kenny as he struggles to process the unfairness of life is resolved, as is symbolised by the way he starts to care about things again, such as getting his dinosaurs back from Rufus.