DC Universe's newest streaming show, Doom Patrol, has officially confirmed that The Flash exists in the shared DC streaming universe. We don't see the character in the flesh, but the confirmation of his existence continues to flesh out the cast of the Justice League in the world shared by Doom Patrol and Titans.
While the continuity isn't clearly spelled out, we know Doom Patrol and Titans co-exist in the same reality because we've already seen them cross over in the early episodes of Titans. Those events are entirely ignored in the pilot of Doom Patrol, however, because the episode's massive time jump glosses over everything that happens up until 2019, including the time Raven and the rest of the Titans met the Doom Patrol and Gar Logan joined their ranks.
Titans already established a fairly thriving Justice League through name drops and other references. In that show, its already been established that the Justice League exists, and at least 3 of the members are DC's trinity of Batman, Superman, and Wonder Woman. This makes Flash officially the 4th League member to be explicitly confirmed for the show. The intro comes when Crazy Jane becomes Baby Doll, who says Cyborg is "way cooler than The Flash."
None of the heavy hitters have been introduced to this universe populated mostly by more street-level heroes, and even Cyborg's powers are inspired by his older incarnation instead of the more fantastical alien technology origin he's had in more recent years. As a result, we don't know just how powerful someone like Superman is, or how fast The Flash is. Cyborg claims The Flash is "really not that fast" when he's trying to impress one of Crazy Jane's personalities, Baby Doll, but that probably shouldn't be taken too seriously as Cyborg was merely trying to puff himself up.
Doom Patrol and Titans both introduced some fantastic and supernatural elements, so it's not hard to imagine The Flash inhabiting this world, although it doesn't seem likely we'll see him on screen soon. The Batman was virtually only shown as a silhouette on Titans, and all other big heroes were simply name dropped or otherwise referenced. With Titans' post-credits scene teasing Superboy, however, it's not hard to assume Wally West could also join the team eventually, bringing another incarnation of the Scarlet Speedster to the small screen with him.
Titans dealt with the sidekicks of characters like Batman and Wonder Woman, so it's no surprise that the show included regular references to the larger DC world, but Doom Patrol doesn't have that same link. Cyborg is the most mainstream character on the roster, so it's not likely we'll see the show used to confirm many more Justice League members. With The Flash getting a major name drop in just the second episode of Doom Patrol, it's certainly a possibility we could get teases for other characters like Green Lantern, or even Martian Manhunter.