So, how do they portray him as being gay? Is he flaming like Jack from "Will and Grace" or is he more subtle in his gayness?
Definitely subtle. Like I said, if it weren't for the gayness he'd be just another add-on character. He's not a "flaming homo". He's just out and honest about it. In fact, the point of the very first story was that Veronica had her sights set on seducing him, something she'd likely not attempt if he were anything like Jack. Nobody knew until he told Jughead.
I guess that makes sense and sort-of follows with what Archie tries to do in their comics. Hell, the broadest stereotype they probably have is Moose as the block-headed jock.