Batman has been referenced in three of the universes
Earth-1 (main universe)
Bruce Wayne exists in this universe, is will known, and lives in Gotham. There is no confirmation of him engaging in vigilante activities.
Oliver Queen: Photos can be doctored. They could have put Bruce Wayne's head on that body. Has Bruce Wayne left Gotham to hang out in Star City recently? No.
Arrow season 6 episode 2, "Tribute"
Additionally, the future newspaper shown in the Flash mentioned a "Wayne Tech" company, which may possibly be associated with Bruce Wayne.
Flash season one, episode one, "Pilot"
Earth-2 (Flash alternate universe)
A character by the name of "Bruce" was found on Earth-2's Barry Allen's phone alongside "Clark" and "Diana". Nothing else was said about him. (Note that Earth-2 Barry doesn't have the speedforce.)
Earth-38 (Supergirl universe)
An unnamed vigilante matching Batman's description was said to have once worked with Superman.
My cousin worked with a vigilante once, tons of gadgets, lots of demons. Vigilantes are nuts!.
Supergirl season 2