There were the same rumors about Randolph Scott and Cary Grant when they were roommates, as well.
I think you're confusing Errol Flynn with Cary Grant. Flynn was a notorious lothario who nailed anything in a skirt in Hollywood, the younger the better, and a notorious drunk as well whose drinking so bloated his once handsome face that it shortened his career by decades.
Grant roomed with Randall Scott when they first came to Hollywood, and then again later after they'd both had success and Grant had left his first wife, and it was rumored they were homosexual, but the rumor has been investigated by several biographers (according to an A&E biography I saw) and the consensus among them is that it's a dubious charge at best, certainly unprovable. Grant's wives, even the two who are still living, never complained that he was gay.