Separate, but not.
After the announcement of actor Cress Williams taking on the role of Black Lightning for the CW, most people assumed that the relatively unknown DC comics hero would be joining Arrow, The Flash, and Legends of Tomorrow in a shared universe.
Unfortunately, during the CW Upfronts, company president Mark Pedowitz told the crowd, “Black Lightning, at this time, is not part of the Arrowverse”. However, there is a ray of light in that statement. Black Lightning won’t be a part of the Arrowverse, but that is just how it is currently. Before coming to the CW, Supergirl aired on CBS and as such, isn’t part of the Arrowverse. This doesn’t mean she doesn’t get to interact with the popular characters, however. Supergirl and the Flash crossed over repeatedly, with the Flash’s ability to travel to other Earths. Supergirl also took part in the big 4-show crossover event earlier this season.
So though, Black Lightning may not be living on the same Earth as any of our current heroes, a crossover is not out of the realms of possibility. Black Lightning will also not be airing during the Fall schedule alongside Arrow, the Flash, Supergirl, or Legends of Tomorrow. Instead, the show will premiere during midseason, with no date yet announced.