Quick Answer: Although Supergirl is about characters from the DC universe, it exists specifically within DC's television universe and not in its films. That’s why despite the existence of Superman within the series, you never get to see more than a glimpse of him. That said, DC's television universe, commonly known as the Arrowverse, frequently has its characters cross over between shows.
No, Supergirl (2015) is not part of the DC Cinematic Universe. The series was developed for CBS separate from the Warner Bros. feature films and exists on its own plane of reality. That’s why despite the existence of Superman within the series, you never get to see more than a glimpse of him. DC does not want two competing versions of the same character on TV and film. If you want to see Henry Cavill in form-fitting spandex, you’ll have to buy a ticket to see him on the big screen.
Melissa Benoist in Supergirl (2015)
Though Supergirl (Melissa Benoist) doesn’t get to rub elbows with Henry Cavill, that doesn’t mean there are no opportunities for crossovers in the DC television universe. On an episode of Supergirl titled “World’s Finest,” Grant Gustin makes a guest appearance as Barry Allen, A.K.A. The Flash. After he accidentally travels across space and time, The Flash leaves his earth and enters Supergirl’s parallel earth. Since the episode aired this March, there are no further plans to do another crossover event. “World’s Finest” was marketed as a one-time, one-way event, meaning Benoist’s Supergirl will not be making a reciprocal appearance on The Flash (2014 - ). At least that is what the show's representatives are saying for now.
Any future crossovers depend on whether CBS opts to renew Supergirl for a second season. If they don’t, there are rumors that The CW will rescue the series and move production to Vancouver—where The Flash, Arrow (2012 - ), and DC’s Legends of Tomorrow (2016) shoot—to allow for easier and more frequent crossovers.
Until that happens, we’ll just have to enjoy clips like this one where Supergirl first meets The Flash.
Aren’t they just the cutest?