No, the Flash is not HIV positive. But, that doesn't mean he can't be schooled on HIV by one of his very closest friends. When discussing his sex life with a gay friend, his friend brings up the idea that the Flash should use condoms, but the Flash thinks that using a condom every time you have sex is only for gay men.
The Flash also happened to be the star of one of DC Comics' PSAs (there was also a Green Lantern PSA), where he helps two gay men who are literally being chased, mob style, by a group of people who accuse them of spreading AIDS. The Flash comes in to drop some knowledge on them.