Why do the duke and the king tell Huck and Jim they are royalty? Why does Huck decide that he does not want to contradict these men, even though he realizes they are lying?

The Duke and the King are charlatans. They enjoy thinking they have tricked people and then they like to take advantage of them. Huck is pretty street-wise. He knows that beneath their jovial lies, these guys can turn nasty and cut-throat. Huck knows it is safer to humor them than offend them.