What is the best way to clear up canker sores caused by braces?

Wax!: Most oral sores associated with braces are traumatic in origin. Wax on the offending wire will do the trick.

No simple answer!: There isn't one remedy or simple answer to this. For some, it is a simple matter of doing a better job brushing and flossing. And yes, it is much more difficult and time consuming to do a good job of it while undergoing orthodontics. Unfortunately for some, it doesn't get any better no matter what until the braces come off at the end of treatment.