The correct answer is it draws a parallel between common swindlers and the townspeople they attempt to cheat.
Indeed, the author is using these characters to convey the message that Southern Society was extremely hypocritical since they pretended to be pious Christians and democratic Americans and yet defended fiercely the pecualiar institution of slavery. Furthermore, to the black slaves, they were akin to some kind of racial royalty and enjoyed a very monarchic supremacy over their slaves.
The Duke and the King are preying on such ethos in order to profit from it.