In the Arrowverse, the Multiverse of The Flash, Supergirl, etc, Supergirl references her cousin "Superman". Does that mean Batman or other DC characters are also there?
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 1, episode 1, "Pilot"
Edit (December 11, 2018): The fact that Bruce Wayne is Batman in Earth-1 has been confirmed during this year's crossover when Supergirl, Green Arrow and the Flash visit Gotham City. Precisely, he was Batman until he disappeared from Gotham City 3 years ago. His cousin is now replacing him as Batwoman, and will have her own spin-off show in 2019, so we may have more information later on. [Edit written by Taladris on ibid's suggestion]
Earth-2 (Flash alternate universe)
A character by the name of "Bruce" was found on Earth-2's Barry Allen's phone alongside "Hal" and "Diana". Nothing else was said about him. (Note that Earth-2 Barry doesn't have the speedforce.)
Flash season 2, episode 13, "Welcome to Earth-2"
Earth-38 (Supergirl universe)
An unnamed vigilante matching Batman's description was said to have once worked with Superman.
Kara: My cousin worked with a vigilante once, tons of gadgets, lots of demons. Vigilantes are nuts!.
Supergirl season 2, episode 7, "The Darkest Place"
James Olsen: So, people see this big guy in this scary mask and they freak out, they run away.
Winn Schott: Just like Clark's friend.
James Olsen: Oh, you mean...
Winn Schott: I feel like they're more frenemies
Supergirl season 2, episode 20, "City of Lost Children"