Standing has always been a useful concept for courts who don’t want to hear or decide on the specifics of a case, to have a convenient way to dispose of the case without having to reach there. So the FBI has been taking NICS check data and cross referencing it to the Terrorist Screening Database for a number of years now.
Here you have two theories of standing. One is that because the cross reference didn’t in any material way affect your ability to buy a gun, you have no standing to sue. Only someone who is singled out for different treatment because of the cross reference has standing. The other theory is that because your purchasing information has been used in a way not authorized by law, that the mere act of having your data cross referenced to another database creates standing in and of itself.
Guess which theory of standing was adopted by the federal courts so far? If that theory holds, no one would have standing since the FBI doesn’t use the screen to influence the person’s NICS status. It presumably just creates an alert. The cross reference might be illegal on the part of the FBI, but no one can challenge it.