I'm not a Flight RN right now, just ground CCT. I don't think fear of flying is a deal breaker though. Heck, I was afraid of flying as a passenger but now I'm working on my pilots license. Exposure sometimes can fix your fears. DO some ride alongs.
Personality wise I think the ability to think and act independently mixed with the ability to know when to ask for help and how to calmly work with your partner is gold.
The main reason I lost my interest to be a Flight RN right now is that the main provider in my area does some crazy schedule like 24work 24off 24 work 24off 24 work 4 off, repeat. I would rather work at McDonalds than be at work 72+ hours a week. I would consider working for one of the other companies that do the standard 48 hours/week, but that's about my max when you factor in training etc.