“Duking it out” and “Put up your dukes” are both expressions from the early 1800s when bare-knuckle boxing was considered a lower-class activity.
When Frederick Augustus, the then duke of York took up the sport, English high society was shocked.
The “Duke” gained so much admiration from the other boxers, however, that they began referring to their fists as their “dukes of York” and eventually as their “dukes.”
And that’s how we got the phrase “duking it out”.