At least for now, the crossover will be one-way only. While it’s likely at least in part a matter of budget (Supergirl is more expensive than The Flash), we’ve been told by sources close to the two shows that the in-universe reason is that Barry Allen/The Flash (Gustin) is able to cross dimensions while, at least for now, Supergirl (Melissa Benoist) cannot. Before fans cry foul, that’s keeping with the current storyline on The Flash, which deals with the aftermath of a dimensional rift opened between “Earth One” and “Earth Two” that is connected to The Flash’s super-speed superpowers.
This has me so freaking excited. I was hoping for a cross-over between Supergirl and the CW shows. With The Flash exploring the multiverse having him appear on Supergirl makes sense, plus the two shows and leads are similar in tone and approach to super heroics. I'm sure this will provide a nice ratings boost for Supergirl. Hopefully, if all three shows get renewed, we can get a big cross-over event with all three shows somewhere down the road.