Keep in mind that your EKG is only as accurate as the doctor interpreting it. While anxiety may not cause a false positive for Atrial Flutter per se, there are many cases of patients being misdiagnosed with Atrial Flutter or Afib, just google it.
As for flying, there are millions of people with heart arrhythmias that fly all the time; having Atrial Flutter should not keep you from traveling. As the previous poster noted, you should discuss with your doc your specific case but having Atrial Flutter or Afib does not mean that you cannot travel and maintain a healthy and active lifestyle.
Jim Harbaugh, head coach of the San Francisco 49ers football team, has Atrial Flutter and he probably flies several times a week. Not to mention that he has one of the most active, high profile, and stressful jobs that one can have.
No it can't. You either have AF/Aflu or you don't.
That said, AF/Aflu can happen intermittently, and when you don't have it, you don't have EKG findings saying you did or did not earlier.
If you suffer permanent AF/Aflu and the heart rate is well controlled, it's completely safe to fly (to take a flight, you can't be a pilot). If you have intermittent runs of arrhythmia which makes you faint or you have other serious symptoms that may make you need immediate medical attention, I would not fly until the situation was under control.
I'd also like to know is it safe to fly if I do have atrial flutter?