The Flash family is one of the largest and most important in the DC Universe, right next to the Bat-Family, but the future of the Flash legacy shows just how important the hero's connections are for the entire planet. When a villain continually reappears for 700 years, it's the Flash Family that finally manage to save the Earth once and for all.
The Flash, more than most heroes, is a generational hero - one who is rooted in legacy. While there have been others to claim the mantle of Batman or Superman, for the most part, the definitive and most common examples of Batman and Superman are Bruce Wayne and Clark Kent, respectively. This isn't the case for the Flash though - many different people have claimed the mantle of Flash over the years, each with equal right to the name. This is likely because the original Flash, Jay Garrick, actually inspired Barry Allen to take on the name despite them existing in different realities, meaning that even the Justice League's resident speedster began his career understanding he was just one part of a legacy.
This idea of legacy being essential to the Flash is shown off in Mark Waid and Mike Parobeck's Flash Special #1. In this storyline, the villain Atom Smasher is prevented from robbing a bank by Jay Garrick, and is sent to prison. Atom Smasher spends the next decade in prison until he manages to escape. Seeking revenge, he finds the Flash, completely unaware that he's now facing Barry Allen, who sends him back to prison. After ten more years, Atom once more escapes, this time battling Wally West. On this occasion, Atom Smasher's powers flare out of control, and he melts into the earth, where he stays for almost 700 years.
There Will Always Be a Flash in the DC Universe
When Atom Smasher finally emerges, it's to confront John Fox, who takes on the Flash identity to finally, truly defeat him after being unable to recruit any of the original speedsters via time travel. Passed down over centuries, the Flash Family's legacy heroes are the most powerful and important in the DC Universe. While Batman's Bat-Family learned from him, no-one has ever truly replaced Bruce Wayne as the one true Batman, but this adventure makes it clear there will always be a Flash to protect Earth, whatever their civilian name. This is likely because Flash is a more hopeful and joyous hero than Gotham's protector, and so passing on the name is more of an honor than a burden. Unlike Batman's protégé Nightwing, Flash has no need to try and help his successors become something better than his own mantle.
The Flash lineage will last for centuries into DC's future, and likely for the rest of time, with the heroes forming a chain of protection that Atom Smasher perfectly illustrates. The legacy of the Flash has been shown to reach far into the distant future and continue to save the world, even after all the original is long gone.