I frequently fly with firearms and ammunition. I follow the TSA rules and regulations and I have never had any problems. I also check the website of the airline (if it's not one that I fly often) and check up on the airlines policy.
I have found the process to be quick and easy.
I do always check with the Texas Department of Public Safety's website to get the latest on states that have CC reciprocity with Texas. I only fly with a firearm to those states. I would never fly to D.C., Chicago, New York, etc. with a firearm. I just don't want to risk the loss of a gun that I like.