why are the king and duke considered criminals

They are swindlers. They were running away from the townspeople. They actually didn't know each other before getting to the raft.The younger man reveals that he was selling a sort of toothpaste. Unfortunately it took the enamel off people’s teeth. The older man held a temperance revival meeting for alcoholics until it was found out that he could drink anyone under the table.

Later, the king and the Duke get their plan to pretend to be the Wilks brothers when they meet the Reverend Elexander Blodgett. He knows the Wilks brothers, and in talking with the King and Duke, inadvertently reveals all the details they need to know to in order to pull off a great impersonation of the Wilks brothers.