One of the aspects of the American Dream is the pursuit of wealth by means of hard work and determination. In his book, the King and the Duke tried to achieve this portion of the dream by alternative means. They would put their lives on the line just to come up with a cleaver scheme in which they could con people out of their money. They created an entire spiel about them being the Dauphin, Louis XVI's lost son in order to go along with Tom and Jim. The two later even went to the extent to put on Shakespearean shows and print out fake "handbills". Rather than actually doing anything useful for society, the two scam-artists tried to take the easy way out of life, but were eventually caught and punished severely. All in all, the Duke and King were trying to accomplish their own small version of the American Dream.
Another aspect of the American Dream is that parents want the best for their children. On the contrary, Pa does not seem to take much interest in Huck. For quite some time, Huck's father disappeared from town only to arrive later when he heard that his son had acquired a small fortune. He then threatens to beat Huck "down a peg" so that he would remind him of his status in the family only hoping to get the fortune for his booze. Things only get worse when Pa learns that Huck has become the first member of the family to learn to read, and consequently takes him away