During the final episodes of "The Flash's" second season, Wally and Jesse Wells were both affected by a second particle accelerator explosion after Harrison Wells attempted to get Barry's speed back. Both were knocked out by the force of the explosion, but neither showed any speedster abilities before the season ended. However, it seems that will change when the show returns this fall.
It's also worth pointing out that, in the Season 2 finale, Grant Gustin's Barry Allen went back in time and prevented his mother's murder, triggering a famous linchpin event from the comics. While we've yet to see how this massive change in the show's timeline will affect the series as it moves into its third season, "Flashpoint" -- the title of the Season 3 premiere episode -- gives fans a major, major hint.
The major DC Comics event from 2011 of the same name saw Barry Allen trying to navigate a totally altered world -- one wherein his mother Nora was alive. As such, it's unclear if Lonsdale's Kid Flash will be a fixture of the world as Barry Allen knows it, or a byproduct of this alternate timeline. Kid Flash will definitely appear in Season 3's debut episode, but it's another question entirely if he'll continue to play the speedster for the rest of the season.