I think it's a typo, but that's just a guess because I've never heard "black burner" used in "real life" (meaning life outside of the Internet) and I've never seen that phrase written anywhere else.

For what it's worth, I read that phrase as "back burner" and didn't realize it actually was "black burner" until you pointed it out.
I guess the poster had "black" people on his/her mind, and that led to him/her typing the word "black" instead of the word "back".

However it came about, it's interesting to think of the implications of "race" [being kept] on the black burner".

That phrase calls to mind James Baldwin's 1963 book The Fire Next Time.