I did one very early in my career. I need more time to recover, so only went with girl number three.
I like the Flirt Flings, and I've been asked by girl number one of I wanted to go once before the second girl comes in, and then the second girl offers as well. I like going when they're both there.
So I would assume you can go three times if you like.
Mileage tends to be very low at Flirt Spa, and in a 20-minute session, you may have even more restrictions.
Maybe someone with more experience with these things could help you better than I can.