Here's a breakdown of his history as the Flash:
* Original Kid Flash: Wally West was first introduced as Kid Flash, a young sidekick to Barry Allen, the Flash. He gained his speed powers after being exposed to chemicals similar to those that gave Barry his powers.
* The Flash (Post-Crisis): After the events of the "Crisis on Infinite Earths", Barry Allen died. Wally West, now a young adult, took up the mantle of the Flash and became the main Flash character for many years.
* Return of Barry Allen: Barry Allen returned from the Speed Force in the New 52 relaunch. While Wally was still a speedster, he wasn't the Flash anymore.
* Rebirth and The Flash Again: In the DC Rebirth relaunch, Wally West returned to the role of the Flash alongside Barry Allen, who remained the main Flash.
So, to summarize: Wally West has been the Flash in multiple eras of DC Comics, even taking on the mantle while Barry Allen was dead and then co-existing with Barry in later runs.