I originally travelled with a poster tube to carry the spars (with a small hole punched in the lid for a spar that didn't fit), and sails in my suitcase. I've also used a larger blueprint / document tube that fits about 3 kites. No questions from the airlines or security. While in Europe and the UK last year, I traveled with two Revs in a single sleeve, and the handles in my rollaboard suitcase. I didn't bring any ground stakes, so I didn't have to deal with checking luggage. No problems other than one security screener asking what was in the bag, and then waving me through.
However, after a few trips . . . I wanted to bring more than a few kites. I traveled several times last year with my main kite bag as a carryon - it's probably about 42" long and maybe 10-12 inches wide / diameter at the widest point. I have only had one comment about it from a flight attendant, and it's always fit in the overhead (at least on Southwest 737s and AA regional jets). No issues so far. My only worry is if they make me check it - then I'd be a bit concerned about luggage handling. Therefore, I always try to get on as early as possible so I can get space at the back of the overhead compartment and pack my regular suitcase in front of the kite bag.