You CAN bring your gun with you when you fly.
Flying with your firearm can be a mess. You have to pack it a certain way and check it in. This video will help!
To read the full TSA guidelines, you can click this link.
After watching this video it seems pretty easy as long as you aren't trying to bring ammunition. Like stated in the video know the rules and laws for the states that you are traveling to. The last thing anyone wants is to run into problems when you land. Worse yet to have charges pressed against you in a state you don't live in. While it is a stretch and hard to account for check the gun laws in neighboring states and states along your flight path. If something happens during the flight or you miss a flight during a layover it would be handy to know.
A hard case is a good idea not just for flying but for any traveling. If I am traveling a long distance to hunt the last thing I want to do is find that my scope has been banged around. One last thing to note that was not mentioned is that the hard sided case does have to be locked and cannot be easily openned.