It seems like it would be a silly form of protest sure, and mean-spirited. But that's not the question. Would it be covered by freedom of expression? After all, I seriously doubt that everyone who ever burned a US flag has "suffered or been persecuted" by the US. And it's not like they have to prove that they were in order for their act of protest to be considered legal.
A couple of American posters here seem pretty confident that burning a rainbow flag would be covered by the First Amendment. Since nobody is citing any cases I'm guessing that it's never come up before the courts, or if it was then it didn't get a lot of publicity. I'm wondering about Canada as we don't have a First Amendment, although our courts have decided that burning a Canadian flag is a legitimate form of protest.