There is no 'requirement', nor is it a normal practice, for FFLs to call in the serial number to the Federal Government on a purchase or sale of a firearm...
However, even a private individual, buying on a face to face basis, is entitled to call their local law enforcement agency to have a description and serial number checked prior to a transfer...The agency has access to the national data base and for peace of mind it's a good practice to do..
Most pawn shops, are required to submit to their local agencies the description of every item that is brought in...Most of the time this is through a computerized data base that LEOs check when a loss or theft is reported...and it that case, if an item turns up, the dealer is out the money paid and the item is recovered, to be returned to the proper owner after the investigation is completed..
We have three gun shops in town and two will accept firearms from out of state individuals with only a copy of a driver's license and one requires receipt from another FFL...It's a personal/professional choice on their parts...