I can't say for sure but I would think you would need a serial number on the receiver since it is actually considered "the" gun; the rest of it is just parts attached to the gun. Just as you can buy any and every part of a gun (except receiver) and have it shipped straight to your door (think parts kit), but if you order a NoDak (for example) receiver it must go through an FFL.
You have to engrave your NFA info on it anyway so if you use a flat, engrave the kits trunnion number on the bent flat. If you use a NoDak or any other 100% that is sent to your FFL you have to use the number t