Well, they are involved in numerous schemes, and Huck himself doesn't want to get caught or blamed for any of them. Plus, he can sense just how far the Duke and King would go in order to maintain their covers and make a good haul, and Huck doesn't want to be caught on their bad sides, because who knows what they could do. Another reason that Huck doesn't expose them at first is that he doesn't really feel like they are doing too much harm, and Huck tends to be a kid who doesn't like to cause trouble. In their last big scheme with the Wilks brothers, you will see Huck's conscience finally kick in, making him want to oust the Duke and King, but before that, the "damage" that they do isn't as personal or devastating, so no real harm done. He says that playing along with them keeps the peace, and
"then you don't have no quarrels, and don't get into no trouble...I hadn't no objections, 'long as it would keep peace in the family...if I never learnt nothing else out of pap, I learnt that the best way to get along with his kind of people is to let them have their own way."
In this admission at the end of chapter 19, Huck lets us know that he knows the "type" of people that these two characters were, types that were like his good old Pap, and the best way to deal with them is to just go with the flow and let them get their way. Otherwise, there was trouble. So, Huck sticks to his instincts and experience, and doesn't get in their way in order to keep the peace and stay out of trouble. I hope that helped; good luck!