One of the most exciting elements of the Legends of Flarrow (my personal favorite moniker for the TV shows Legends of Tomorrow, Flash, and Arrow) is the way that the shows are closely intertwined. Unlike your average "connected" franchises (*cough CSI), the characters aren't limited to an official crossover episode once a year.
Instead (or perhaps more accurately, in addition to), the characters often wander from show to show, helping out for big battles, coming by for celebration or for mourning, sharing technology, and generally just staying in touch at all times. Legends of Flarrow has even brought in a DC character from a cancelled show on another network, when Constantine (Matt Ryan) dropped in on Arrow.
With all this constant mingling of shows, it's no surprise that there have been many fan rumors about the possibility of another DC series joining in on the fun. Supergirl, currently in it's first season on CBS (and only recently picked up for a full season, at that), is regarded as prime crossover fodder, especially as creators Greg Berlanti and Andrew Kreisberg are involved in all four shows.
However, fan hopes that Kara Zor El might be flying over to Central or Star City in the near future were put down by showrunner Kriesberg in a recent interview with The Hollywood Reporter.
There's always those late nights, delirious, semi-high on pizza where you're like, 'You know what would be really cool? If …,'. But right now there is no legitimate actual plan to bring [The Flash's] Cisco [Carlos Valdes] onto Supergirl or to bring [Supergirl's] Winn [Jeremy Jordan] onto Legends [of Tomorrow]. First of all, we don’t even know if we could, legally.
The most interesting part of this little statement is that Kriesberg brings up the potential legal issues with creating a crossover. On the face of it, this shouldn't be a big deal. While the shows are on two different networks, CBS owns the CW, which would negate any issues there. The creators are clearly enjoying the idea of a potential crossover, and there has been talk of crossovers for promotional purposes. On a practical level, they both film in the same city, and on similar schedules, so that shouldn't be an issue either.
So what's holding them back? Presumably, this would be a rights issue, which makes it incredibly complicated. We know that the Flarrowverse is entirely separate from the DCEU, but it hasn't been made entirely clear where Supergirl fits into the film universe. Superman exists in the Supergirl universe, but we never actually see his face, and Supergirl lands on Earth when he is already established. It could well be that Supergirl will become (or already is) connected to the DCEU, which would make her appearance in Flarrow extremely complicated.
This may also be a situation where Flarrow is unable to legally mention Superman by name, and the inclusion of Supergirl would be making that omission just a little too obvious. As it stands, Legends of Flarrow viewers have caught a few easter eggs relating Superman (and Batman), most notably in the recent Legends of Tomorrow trailer. We've also seen some characters from the Batman mythos appear in their entirety, while others (such as Harley Quinn) were legally only allowed to be teased. With so many live-action variations out right now, the details of how each character may be used are extremely complex.
While there may be no concrete plans to combine the shows at the moment, it's clear that the showrunners are still interested in the idea of it, and it's not off the table entirely. Even if legal issues do make it impossible, the Legends of Flarrow-verse will undoubtedly continue to grow, creating even more incredible new superhero shows for the small screen.