By prohibiting anyone that is on the "no fly list" from lawfully purchasing a firearm, wouldn't that be a violation of rights as protected by both the 5th and 14th amendments to the US constitution? Since there is no way to know that one is on the "no fly list" until one is prevented from flying, and there is little to no way of appealing the decision of having one's name added to the "no fly list", this would be a CLEAR violation of one's rights as protected by both the 2nd, 5th, and 14th amendments.
"I'm sorry sir, but your name is on the no fly list. You are not boarding the plane and guess what, you can no longer purchase or own firearms!"
"How did my name get on the no fly list?"
"I'm sorry sir, but that information is classified."
"Who do I talk to about getting my name removed from the no fly list?"
"I'm sorry sir, but that information is also classified. Have a nice day sir!"