There's this expression shown in Oxford:
have — going for one
Used to indicate how much someone has in their favour or to their advantage.
Why did she do it? She had so much going for her
In this expression, the pronoun coming after for always refers to the subject.
In the following 11 examples of the Oxford Dictionary, there's no example of a reflexive pronoun after for. Plus, the title of the expression has one instead of oneself.
So, I take it that you cannot have a reflexive pronoun come after for.
But then, there are numerous counterexamples of a reflexive pronoun coming after for in news articles and books:
...she was using blackorwhite thinking when she told herself that she had nothing going for herself... (book 1)
I'm not making any excuses for her but for a woman with so much going for herself Trevonne has low self esteem. (book 2)
One thing she had going for herself though was drive. (book 3)
Plus she had a lot going for herself. She was intelligent, funny, caring, ... (book 4)
Tonya makes it clear that skating was the only thing Harding had going for herself. (news article 1)
Even her attempt to have something going for herself outside the house, some kind of passion and hobby, got painted as tone deaf and self-indulgent... (news article 2)
So I wonder whether a reflexive pronoun in this expression is admissible.