I think they would get along very well, with the same type of older/younger superhero relationship as Kara/Supergirl and Nia/Dreamer have. Both Brec and Melissa B. are sweethearts in real life, and their characters reflect that. And I think that Alex and Pat would also work well together.
As soon as I have time, I'm going to write a fan fiction story in which Supergirl tracks down Lex Luthor in Blue Valley, and unexpectedly runs into Stargiirl in action. (Courtney doesn't know who Lex is.) Then they join forces to defeat Lex and his cohorts in crime.Their first meeting would be mostly the same as the Flash meeting Supergirl in the Worlds' Finest episode in Season 1 of Supergirl, except that "ace reporter" Kara would be expected to have already heard about reports of a new superhero operating in the area. And I would expect that Supergirl would be well-known throughout the country, but Courtney is shocked to find out that Kara = Supergirl.