The notion of applying the no-fly list to NICS checks has an unintended consequence: subsequent litigation will compel revealing the content of the no-fly list and how names are put on it - something TSA et al have STRONGLY & successfully resisted doing so far. They REALLY don’t want to reveal anything about the no-fly list.
Precisely. The no-fly list is an extra-legal instrument that wouldn’t stand the test of accuser-defendant-trial-judgment dictates of standard US law.
It is a wholly capricious mechanism that is implemented via a variety of means which would not survive evidentiary standards. In short, it is willy-nilly and in this administration - political and ideological.