there is no gun show loophole. any person buying from a FFL dealer legally has to undergo a background check. the private sales that happen at gun shows happen more commonly outside of them. i live in kentucky which ranks 5th in the country for gun owners and allows for private sales(the thing you are referring to with gun shows) and the guns with black boxes around them were bought at gun shows and i was required to fill out a 4473 and undergo a background check for each one. the guns with red boxes were bought via private sale and i did not have to go through the background check, BUT everyone i bought them from either knows me very well or made a bill of sale to prove i was the owner of said gun. sure someone who cant legally own a gun could go through a private seller but it is illegal to knowingly sell a gun to a felon or other person barred from gun ownership.

Purchasing firearms from private citizens requires no background check nor 4473. There is no "gun show loophole" outside of a liberal gun-grabber's fantasies. Every new gun in the US, when sold legally to a private citizen, requires a background check. No exceptions. What the “loophole” refers to is the fact that in some states (not all) private person-to-person sales can be performed without a background check. It just so happens that some of these are performed at gun shows, but the actual number is very, very low. Any gun you buy from a dealer at a gun show will require a background check.
Additionally, there's an amendment in the constitution which explicitly states that state laws / local laws cannot be less restrictive than federal law.