It's an interesting question that other posters have answered, so the only other thing I would add is that Flagg's ambiguous race fits well with his evil nature (thinking specifically to the pamphlets he carries with him). He is pure evil, pure hate regardless of gender, class, SES, etc . . . and his ambiguous nature allows him, as the novel notes, to run with the KKK on one hand, and Black hate groups on the other. There's even the quote: "his claim that he was black man had never been disputed, although his skin was very light" (217). It seems Randall illustrates the fact that extremism across identity spectrums is the same (motivated by unthinking hatred).
To add further complexity to the discussion, you might consider Mother Abigail as a contrast (in so many ways, but race being one) to Flagg. If I am correct, while the survivors see a 'black woman' in their dreams, her race is ambiguous (she could be racially Black or symbolically black). In fact, Flagg is even mentioned in one dream as the black man (thus setting up the potential for reading the symbolic 'darkness' in both characters rather than race). Yet, when Mother Abigail is first introduce to the readers in the uncut version in chapter 45 (i.e. when the narrator gives us insight into her thoughts), she is not called the 'black woman,' or even African American. Instead, her race is revealed when she reflects on ancestors who were enslaved, emancipated, and then started the legacy of Sweet Home. I.e. race (Blackness) is untethered from evil (blackness) as an identity marker. I think it's a brilliant act of characterization that plays well with SK's skill with contrast/foils.