Quick Answer: Although The Flash is about characters from the DC universe, it exists specifically within DC's television universe and not in its films. That’s why you will never hear characters on The Flash talking about Superman or Batman’s recent cinematic showdown. That said, DC's television universe, commonly known as the Arrowverse, frequently has its characters cross over between shows.
The short answer is no; the series exists on its own plane of reality within the DC Comics family. That’s why you will never hear characters on The Flash (2014 - ) talking about Superman or Batman’s recent cinematic showdown. It’s also why there will be another actor, Ezra Miller, playing The Flash on the big screen. This is in stark contrast to Marvel’s Agents of SHIELD (2013 - ), a series that often references events in the Marvel feature films and is meant to exist alongside them in the same universe.
However, The Flash is a part of the growing DC TV universe on The CW, or Arrowverse, as it is commonly referred to. Unlike Marvel’s coexisting TV and film universes, those of DC remain totally separate. To date, the Arrowverse contains its mother show Arrow (2012 - ), from which The Flash was spun-off; DC’s Legends of Tomorrow (2016 - ), another direct spin-off from both Arrow and The Flash; and Vixen (2015 - ), an animated series for the online streaming platform CW Seed whose title character made a live-action appearance on Arrow.
The Flash (Grant Gustin) on Arrow (2016)
The Flash is also loosely tied to Supergirl (2015) following a one-time crossover event. On the Supergirl episode “World’s Finest” that aired on March 28th, 2016, Grant Gustin appeared as Barry Allen/The Flash. Barry’s appearance was made possible due to the multiverse theory introduced on The Flash. Barry is able to travel between parallel dimensions — Supergirl existing in one of these dimensions — that exist within the multiverse. In real life, however, the logistics were more difficult, as both series shoot in different locations (Supergirl in LA, The Flash in Vancouver) and air on different networks (Supergirl on CBS, The Flash on The CW). At the moment, there are no further plans to cross the series over again. That decision, it seems, depends on whether CBS renews or cancels Supergirl. (There are some rumors suggesting that The CW could rescue the series and move production to Vancouver should CBS cancel it.)
The Flash (Grant Gustin) on Supergirl (2016)
Until then, we’ll just have to hope, pray and simply enjoy watching Arrow's John Diggle freak out when he sees Barry running at super speed.
Aren’t crossovers the best?