I sometimes forget how the Young Justice show makes people think Barry was kinda and responsible when it came to Wally becoming Kid Flash. In the show, Wally asks Barry, Barry says no, Wally performs an experiment on himself to get powers and ends himself up in the hospital but with powers, and then Barry reluctantly agrees cause... well, he has powers now. In case any of ya'll are wondering, it ain't like that in comics lol.
See in comics, Iris leaves Wally, who is visiting from Nebraska, with Barry while she does work and Barry, who knows Wally is a superfan of the Flash, tells Wally he is friends with the Flash and so has the Flash show up. Weirdly so, there is also the side fact that Barry has a lab in his apartment, but that's not important. Anyway, Barry manages to introduce him to Flash without revealing to Wally that Barry is the Flash. Barry tells Wally how he got his powers in a freak accident, and it is a one in a billion chance, lightning never strikes in the same place twice, and BOOM! right in front of his eyes, Wally gets hit by lightning, and chemicals drop on him, and Barry is shocked. Mind you, Wally is fine, no hospital, he's just wet lol. Barry is basically like, "Omg, do you have powers now???" and Wally is like, "Omg, I guess I do!" and then Barry takes him to play catch. While they are out, Barry runs into a villain and just leaves Wally to the side. Wally sticks his nose in the situation and gets shot at, but he's a speedster, so he catches the bullets (makes MCU Quicksilver so much more embarrassing). They go back to Barry's place right as Wally tries to call out to Iris and Barry is like "Uh no, secret ID" and tells Wally he seems like a responsible kid, which is good cause he has an incredible gift. But! He better use it for good. Wally promises, and then Barry is like, "And you can't tell anyone," and Wally is like, "Okay, fine," and Barry gives him a shrunken Flash suit, and that's how we get Kid Flash! Barry... did not even make an attempt to be responsible...