If at anytime a U.S citizen has been placed on the no fly list, the should not be eligible to purchase a weapon

In the recent events regarding hate crimes towards minority groups in the united states, some level of restriction needs to be placed on the weapon distribution industry and the steps necessary in order to purchase a weapon, such as past federal offenses, run ins with the FBI, suspected allegiances to terrorist groups, placement on government supervision lists, justification for being on said list, and probable cause for suspicion regarding observation by local authorities or those of higher authority