5 years ago - 12-year-old Bart Allen is sent back in time so Wally West can bleed off his speed force powers. He is adopted by Jay Garrick, becomes Impulse, and joins Arsenal's Teen Titans.
3 years ago - 14-year-old Bart is recruited by Cyborg into the new Teen Titans. After he is shot in the knee by Slade Wilson, he chooses to become Kid Flash.
1 year ago - 16-year-old Bart joins all the surviving Titans on the homeworld of the Titans of Myth to save Donna Troy.
2995 - Bart Allen is born with a hyper-accelerated metabolism. He is placed into a virtual reality to keep up with his accelerated growth.
2997 - After aging 12 years in 2, Bart's parents go to Querl Dox, who sends him back in time so Wally West can bleed away his residual speed force energy.
Bart Allen is an incredibly fun character, someone hugely important to the story of his entire generation of characters, but his origin is an absolute nightmare. We're trying to AVOID time travel, and for his story to work there have to be two major time travel elements.
We've already established that there are only two functional time travel techniques that will operate in our new DC Universe without completely ending the timeline of the original time traveler; Rip Hunter's timesphere and Brainiac 5's hypertime theory. Barry Allen's death occurred when he tried to save Iris Allen from Professor Zoom, fleeing into the Speed Force where they were both dispersed. It simply needs to be allowed that Barry managed to drop Iris back into the timestream, where she became a resident of the 31st century and gave birth to Barry's twins; but for Barry's sacrifice to mean anything, he can't have survived that trip as well.
Which explains Bart's existence in the 31's century. the idea of his hyper-accelerated metabolism is a really cool idea, and the family going to Brainiac 5 to send him back to the past where Wally can save his life is a fantastic explanation for Bart being sent back to our time. It's one of those rare absolutely necessary time travel elements that don't really need a huge amount of rewrite to make work, and thankfully don't even confound the story that much, as Bart doesn't have any memory of future events.
A major element of Bart's story is his accelerated aging into an adult and taking over as the Flash, but that story was redacted so hard the entire series was canceled, with the earlier Flash series restarted with the original numbering. We're clearly not bothering to include this, or Bart's subsequent death and rebirth thanks to more time travel and multiple-world nonsense... We'll just keep him the way he is.
This last picture is actually Wally West's costume from the Young Justice animated series. You can usually tell the two Kid Flash's apart by their hair color. It's incredibly hard to argue with the cleverness of this costume, to the point that this is clearly the outfit Bart should be wearing when he takes over as Kid Flash.
The Impulse identity, meanwhile, is clearly meant for Wally's daughter Iris. The Flash identity is one of the strongest legacies in DC, and all these characters are as much a family as they are a team.