Origins from New 52's main earth
During a visit to the Central City police laboratory where Barry Allen worked, the freak accident that gave Allen his powers repeated itself, bathing Wally West in electrically-charged chemicals. Now possessing the same powers as the Flash, West donned a smaller sized copy of Barry Allen's Flash outfit and became the young crimefighter Kid Flash. Wally had a strained relationship with his own parents and often looked to his beloved aunt and uncle for moral support and guidance.
At one point in time, Wally became a founding member of the original incarnation of the Teen Titans, alongside Robin (Dick Grayson), Aqualad (Garth), Omen, Speedy, and Wonder Girl. One day while fighting alongside the team, Wally disappeared. At this point, Wally was cast into the Speed Force by Abra Kadabra and forgotten by everyone.
While trapped in the Speed Force, Wally sensed a presence, who he realized was a being from outside the universe, and learned that this being was watching the universe, and was responsible for preventing the timeline from re-forming correctly after the Flashpoint, by removing a decade from history. Wally, observing the universe from the Speed Force and with his regain pre-flashpoint history memories, repeatedly tried to break through to warn that world's heroes of the impending threat. None of those heroes remembered him, however, as in their timeline they'd never met him, as Wally had been erased by Abra Kadabra. Just before he fully faded away to become one with the Speed Force, however, Barry Allen remembered him and pulled him out, saving him. Wally told Barry about the history that was lost, and the Flashpoint, before leaving to gather a team, the Titans.
In Young Justice
Wally discovered his uncle Barry Allen was The Flash. Being the Flash's biggest fan, he begged his hero to let him become his sidekick. Barry refused, but that didn't stop Wally. He replicated the experiment that gave Barry his powers in his family's garage. He blew up the garage and ended up in the hospital. Barry felt guilty for leaving notes that Wally could work on.
After he came out of the hospital, Wally manifested the powers he desired. Barry reluctantly agreed to let him become Kid Flash, but only if he did exactly as he said. He became a superhero in 2008.
In "LEGO DC Super-Villains"
The Flash (Wally West) can unlock during free play of Level 3 from Story Mode, and Young Justice version of Wally West can unlock after finish Young Justice DLC level "The Summit".