Poor lost soul here is some clarification.
C3 dealer in NFA firearm other than destructive devices.
AR15 typical semi auto firearm if barrel is 16" or longer does not need go through C3 dealer but any dealer can sell.
LEOnly AR15 would be a semi auto post 94 assault weapon that a FFL dealer C3 or not could sell to a LE officer if he has a "For Duty Use" request on Police Dept. letterhead signed by a commanding officer. The officer could privatly purchase this weapon. The officer could privatly register this weapon on form 1 as a short rifle less than 16" or purchase a less than 16" rifle in LEonly config. from a C3 dealer on a form 4.
Fully Automatic Weapon transferable could be purchased from C3 dealer or individual in his state of residence on a form 4 but this would not be an LEonly gun as anyone could own it, or from Government agency within his state of residence on a form 5 but once again not an LEonly gun. Anyone could do this.
No you as an individual officer can not purchase a post 86 Dealer Sample machinegun. This would have to be purchased by a Police Dept. not an individual officer then the Police Dept. could issue this to you as a duty weapon but you could not take personal ownership of this weapon ever.
Your post is confusing, because of your terminology.
AR15 typically thought of as semi auto?
LEonly AR15 post ban assault weapon to be purchased by LEofficer with dept. letterhead neither of these would be a form 4 gun.
No need to go through C3 dealer on this unless a short barrel was being purchased, this caused confusion, this short barreled LEonly AR15 semi would be a form 1 or form 4 gun.
Hope this makes it all clear as mudd.