Have (something) going for you is and idiomatic expression from the early ‘60
If you have something going for you, or if something has something going for it, there are certain advantages that will make the end result successful:
- They've got a happy marriage, great careers, wonderful kids - in fact they've got everything going for them.
(Cambridge Dictionary)
Have (something) going for one:
to have a talent, skill, etc., that helps one
- She's not as young as some of the other athletes, but experience helps, and she has that going for her. You should be more confident in yourself. You have a lot going for you!
(M-W)
Usage as evidenced by Google Books is most often correct with only a few instances of the use of the reflexive pronoun and all main dictionaries don’t use definitions or usage examples with reflexive pronouns.
I’d avoid using the reflexive pronoun even though the meaning is clear, so we could say that its usage is non standard.