Dealing with a superhero who has a legacy can be a bit of a pain as this thread has demonstrated, since there's room for disagreement about which character best represents the hero. It's a problem that to my knowledge Marvel doesn't really see much of (outside of stuff like "which X-Men team is the ultimate one?"), but it's very much an issue within DC fandom, particularly with The Flash.
And that is why I think the best route to go is a passing of the torch story, kind of like Mask of Zorro. There are a lot of different ways they could approach it too, which is part of why I think there's so much potential to be had.
Option 1: Prologue features Barry as the vintage Flash with a young Wally as Kid Flash. Wally has to hang up his Kid Flash tights and live a "normal life." In act one, we jump ahead to "modern times," where a solo Barry Allen flash comes across a super villain plot. The villain kills Barry, and when Wally learns of his uncle's death, he dons the costume to pick up Barry's trail and beat the bad guy.
Option 2: Same as above, except that the reason Wally stops being Kid Flash is because Barry dies while stopping a supervillain, and Wally hangs up his costume because he doesn't think he can go it alone. Years later, the world needs The Flash again, and he resolves to put on his uncle's costume and give the people the hero they need.
Option 3: Barry dies while Wally is a teenage "kid flash," and we get to see the awkward transition between being a teen sidekick and a full fledged superhero. We get to see Wally putting on the boots before he's even sure he's big enough for them, while dealing with the loss of his mentor.
These are just a few examples. There's a lot of places they could go, but I'd wager that the potential for this kind of story is far more interesting than a typical origin story. All we really need to know is that they were both involved in a laboratory accident that gave them speed powers, possibly through a flashback (heck, they could even try to make things more believable by having them get their powers at the same time from the same accident). The real origin story though would be about Wally taking up the mantle of a hero that came before him, and coming into his own as the hero of a new generation. They could even have some humor about fanboyism, hehehe.