Model 1816 Flintlock Muskets made in the years 1832 through 1840 were classified as First Class Arms and held at the various Arsenals and both National Armories, Springfield and Harpers Ferry. These muskets were to be issued only upon direction of the Ordnance Dept. Some were indeed issued during the Mexican War as M1816 Flintlock Muskets were used to fight that war, not the Model 1842 Percussion Musket. Springfield Armory had produced 113,600 Model 1816 muskets, 1832 through 1840. Of that number, 86,565 were converted to percussion in the 1850-1853 period. More may have been altered in succeeding years to the Maynard tape priming system in 1857-1858.
Type III Springfield M1816 muskets in their original flintlock condition are very rare. There are five in the Springfield Armory Collection. I know of less than a dozen in private collections. Those that have survived show signs of being issued. In the antique gun market there are a great many reconverted examples. Some are good recons others are laughable.
The 1833 dated musket pictured below is in original flintlock condition and was issued. It has a rack number on the barrel to the rear of the proof and viewing stamps. There are three other 1833 dated Springfield M1816 Flintlock Muskets having a two digit rack number stamped in the same area of the barrel using the same size and font numbers. All of those muskets are in their original condition.