My guess is that it would not be alright. If a nail file can be used to stab somebody, then so can a pivot rod from a sax. Even a flute head could do a lot of damage, thrust into a face. USA seems to be ultra-cautious since 9/11.

I recently flew to Spain/Portugal and back with my flute, and I had no trouble at all. Nobody at security or customs even asked about it. I recommend keeping it with you as a carry-on inside of a backpack or something. That way, it`s available if they want to look at it. I definitely would NOT check it with your luggage! The change of heat and pressure inside of the plane (not to mention the way things get thrown around in baggage) are sure to damage your flute.

These is all very good points, and they are helping me make my parents let me take my flute in a carry on bag instead of in with my luggage. thank you for you information.