Is it legal for someone to date while they are going through a divorce?

It is still called adultery. There are still laws on the books in many states about adultery but there is not the enforcement overall that there used to be. HOWEVER, that is going to depend on your state and how your state views adultery.

You can view the various state's laws on this site:
State Adultery Laws

Read how the law applies:
Adultery - By Franklin Foer - Slate Magazine