What connection does Huck see between the duke and the king and real royalty? What might Twain's opinion be?
Some of the most brilliant characters in Mark Twain's The Adventures of Huckleberry Finn are the King and the Duke, two con men claiming to be European royalty who swindle several communities during the course of the narrative. While the two men aren't actually royalty, Huck assumes that they're similar to the real thing. By extension, we can surmise that Twain himself regards royalty, and political leaders in general, as little more than dishonest crooks worthy of derision.
The key to this theme in the novel can be found in Chapter 23 ("The Orneriness of Kings"), in which Huck and Jim discuss the criminal activity of the Duke and the King. At one point, Huck says, "'all kings is mostly rapscallions, as fur as I can make out" (153). With this quote, Huck suggests that the atrocious behavior of the King and the Duke is relatively analogous to the behavior of real royalty. Thus, in this situation, we can assume that Twain's opinions are similar to Huck's opinions, and that the author views royalty as con artists who take advantage of hard-working, honest folk.
Huck is willing to go along with the expectations and requests of the "duke" and the "king" for the sake of keeping peace on the raft, but he has doubts about their authenticity from the beginning. As time goes by and he and Jim get more opportunities to observe their behavior, Huck becomes thoroughly disgusted with the pair.
After they ended the performance stand of David Garrick the Younger and Edmund Kean the Elder, Huck and Jim had a quiet conversation while their "royalty" slept. Huck took the opportunity to express his opinion of royalty in general, which matched Twain's thoughts about the idea of systems and families as monarchy.
All I say is, kings is kings, and you got to make allowances. Take them all around, they're a mighty ornery lot. It's the way they're raised.