Is there a site you can enter a serial number for a gun and get its history?
No. If you know the manufacturer and model some information may be available. Several enthusiast sites have lists that identify the year of manufacture by serial number for some popular models. The Springfield Research Center site has compiled a very incomplete list of serial numbers that have verified military history, but even there a hit will probably only give a date it was issued, inventoried, or disposed of by a unit.