Jerold - Here is one possible way that Flintlocks could have been issued to the 32nd Tenn.
In 1861, after the seizure of the arsenal at Batton Rouge the Confederates found 8283 flintlock muskets in stock as part of the arms there.
5000 of these were sent to Mississippi - Unconverted - leaving 3283 muskets. These were to be sent to the Mt. Vernon arsenal for conversion. However, they were waylaid in Memphis before they could reach their destination.
On June 7th, General Pillow wrote to the Sec of war asking for the use of these 3200+ guns for immediate issue to the forming Tenn regiments. 1200 were set aside for this use and were issued to two Arkansas regiments. On the 11th of June and again on the 20th, Pillow again wrote and requested the additional 2000 guns.
Eventually these guns were transfered and at least some of them went to the 23rd Inf and some ended up with the 38th. What I do suspect is that the flintlocks may have been issued - and turned in as soon as better arms were found - and then re-issued to newly formed groups. (this happened to the flintlocks of the 38th when they were replaced in early 1862) Maybe the 32nd were issued some of these guns and just had the misfortune to get in a fight before they could get better arms.
All of these should have been 3rd class marked muskets and dated between 1812 and 1820 - or have been in a previously used condition (Seen earlier service)
Interestingly, there is a known gun - of all things a Pulaski Armory Rifle - identified from the Ft. Donaldson period - from the 32nd. The name on the gun identifies it to a First Orderly Segt. of Company G named Arrowsmith. Segt. Arrowsmith was captured and exchanged at Ft. Donaldson and his 1861 dated gun may have been kept as a war trophy.
Perhaps there was a mixed bag of arms in the 32nd. With some of the flank companies having other arms etc.
Hope that this is of some use to you - Tom