Unlikely.
The linked Genius annotation seems to be the source of this claim - it was posted in September 2012 by a user with no other contributions to the site, and has since been copied verbatim to other places, such as Quora.
It's hard to prove a negative, but searching has not turned up any other mention of "red, gold, and green" being used as a gay pride symbol. Multiple respondents to the Genius annotation have also been unable to verify it:
I won’t say it`s wrong, but I looked for it, and I couldn’t find anithing [sic] about that or a picture of the flag, where did you get this info?
A red, gold, and green flag is, however, one of the symbols of the Pan-African movement. A more common claim - posted twice on the Quora thread, and as a proposed edit on Genius - is that Boy George was attempting to draw a parallel between the struggle for racial equality and the struggle for gay equality, but whether that's true is probably a whole different question.
Furthermore, the quote from Genius claims that the rainbow flag was not in use during the 80s, which isn't true: it was invented in 1978, five years before "Karma Chameleon" came out.