Can I just say this first: Those two look ADORABLE and I am TOTES shipping them already.
The answer from Greg Berlanti, who serves as producer for both shows: You’ll have to wait and see.
“The network has said publicly at this point they’re going to keep her to themselves. I always approach the shows as a fan first, so I would love to see (a crossover). I think in success, all things are possible. But there’s a lot that would have to happen before everybody might say yes to that.”
The whole process is likely complicated by the fact that The Flash and Arrow are both at The CW, while Supergirl is at CBS. So all we can do is root for the success of Melissa Benoist’s Supergirl, to give them the incentive to work it out.
In the meantime, forget Iris, Barry! The Flash and Supergirl were clearly meant to be together. Your costumes are even colour-coordinated!