I think there are several ways this question could be answered, however through my research and in my opinion the central problem (conflict) in Huck Finn is Huck's struggle to figure out for himself whether or not slaves are people or property.
While Huck is friendly with Jim at the beginning of the novel, he still calls him the N word, and treats him like a child. Huck was taught from early on that blacks were inferior, and even though he didn't treat them badly, he thought that abolitionists were horrible because they were breaking the law and stealing other white people's property.
As Huck and Jim travel down the Mississippi River, they have fun, but Huck humiliates Jim by making him dress as a sick Arab, he puts him in danger by bringing the King and the Duke on board the raft, and he nearly sells him to slave traders who come near the skiff.
However, the turning point (and resolution) of the novel comes when Huck tries to play a trick on Jim by making him think that he had died. Jim was so hurt and angry that Huck would do that to his "friend" that Huck finally realizes that despite their color differences, that Huck and Jim are indeed friends...and equals.