I have flown multiple times with 3 and 4 piece fly rods without any trouble. Immediately, after 9/11 they would not permit reels with fly line in place, as carry on, but that is no longer a problem. They still will not let you carry your flies in the cabin. Enjoy your trip.
TSA has changed a lot. I routinely tie flies while flying. They allow small scissors and other tying tools... and they have no problems with hooks or flies in the cabin.
