I've had minimal problems traveling with firearms. Whenever I go even if I don't have one with me I bring a lockable case so I'm all set if I buy one. One of the things I've done at check in is show them a copy of my C&R FFL and after that I'm good to go.
I only had a problem one time and I was sent to TSA. I had to clear with the supervisor and he was OK after I did a verbal appraisal of a couple of his firearms for him
Jim