From the outset, Huck and Jim are ambivalent and somewhat distrustful regarding the King and the Duke. The wild lies that seem to leap from both men constantly are subtly recognized for what they are - lies - by both Huck and Jim.
Even though he is aware of their true characters, Huck plays along...
For his part, Huck is caught in a (familiar) dilemma. He helps the King and the Duke in the first place because they quite simply were in need of help. Once they board the raft, they become part of Huck's "group", for lack of a better term.
Huck's social code clearly suggests that betrayal is unacceptable. Abandonment is an infraction of the code as well. It is in this way that Huck finds himself in a position demanding his loyalty to these two crooks.
Huck does not like the con men. He does not respect them, except for their exceptional abilities to dissemble and lie. In this area, Huck recognizes their virtuosity with astonishment. Yet, these are not skills that Huck truly admires, though he does recognize the ability to lie as a skill.
Beholden to a social/moral code that compromises him, Huck cannot betray the King and Duke in good conscience. Additionally, he is worried that Jim may come to harm through the two men.
This worry is a facet of the broad social-value system that places white males at the top of the social spectrum. Huck and Jim are socially less powerful than the King and the Duke and have been conditioned to respect, fear, or otherwise heed those above them in the social hierarchy.