Yes, we should make sure that when a person attempts to purchase a firearm, They are checked by the FBI, but that is already under law and being done.
The failure in the Texas church shooting, The shooters criminal background was not disclosed by the US government - US Air force, My understanding is, This is under investigation as told by the media.
Take the Las Vegas shooter, He had no criminal record, He filled out the FBI required paper work, Submitted his legal drivers license. everything to , he had no criminal record, was not under an investigation and ect, So he acquired his fire arms legally, My point, The man had NO criminal record, Not under investigation, no nothing. what more could have been done to establish that this man could, or could not purchase a fire arm???
Criminals will always get fire arms, the black market meets their demands easily.