It really should be no surprise that Supergirl is going to have a crossover with The Flash. This was something that was rumored back when Supergirl was first announced, and it is coming to pass. However, what form is this crossover going to take? Considering that the DC comic universe that inspired both of these shows are famous for exploring time travel and alternate timelines, this could signify a change to both shows.
The Flash and Supergirl crossover will happen on Supergirl's show that will air on March 28, 2016, according to ScreenRant. The issue is how this will work, as The Flash is essentially a spin-off of the DC universe established on the show Arrow. Now that this shared DC universe is growing with DC Legends of Tomorrow, it was only a matter of time before Supergirl entered the mix.
As it is, the Supergirl show has a Superman problem as the character only appeared in shadow and no face shots on the pilot episode. Supergirl has expanded its universe by introducing J'onn J'onzz, the Martian Manhunter from the Justice League comics into the show as a central character.
The issue that this episode, called "World's Finest" (an allusion to a comic where Superman and Batman used to team up) isn't an establishment that both shows take place in the same universe. The imdb summary describes it as: "Kara gains a new ally when the Flash arrives from an alternate universe and helps her fight the Silver Banshee and Livewire in exchange for her helping him return home."
Yes, it looks like The Flash will be travelling to an alternate universe to meet Supergirl. If you know anything about the DC Universe, this should not come as any surprise. After all, the comics established the existence of a multi-verse decades ago, and then eliminated that in a famous series called Crisis on Infinite Earths. Then the multi-verse was reestablished again in another series called Infinite Crisis, and that could probably be revised as well because...yeah, the DC Universe is confusing because, like most comics, they tend to rewrite the universe every once in a while.
The issue is that DC's Legnds of Tomorrow as well as elements of The Flash have introduced concepts like time travel and parallel worlds. Therefore, if The Flash and Supergirl crossover becomes popular amongst the huge fanbase, the shows could write up some huge event where the world of Supergirl and The Flash could become one. In fact, that could totally be a ratings-booster.
This is assuming that Supergirl will have a second season, as it was not really well-received last year. It is possible that this crossover episode is an attempt to boost ratings, and it probably will work.
It is pretty safe bet that the Flash, the fastest man alive, and Supergirl, the Maid of Might will have some kind of race. DC has been famous for having race between Superman and The Flash, so I don't see how the writers can resist that.