Many rifle companies were issued horns and they are carried on Ordnance Returns at least as late as 1805. The Return of Ordnance, Military Stores, Clothing and Quartermaster's Supplies at the Schuykill show 118 powderhorns with straps as well as 293 stoppers fit for service and 703 powderhorns damaged and unfit for service.
I'd say as far as military use, horns and flasks would have been worn on the right side the same as cartridge boxes, as riflemen used the same manual of arms and often fought as line troops. Early riflemen didn't carry bayonets and the loading procedure was a little different, but other than that they did the same things as everybody else.
In 1850, there were purchased or fabricated at the arsenals 2,000 copper powder flasks as well as 2,000 flask and pouch belts. The money used for this was from the appropriation for arming and equipping the militia. The Ordnance Reports of 1850 and 1851 are very interesting. It was a very busy time in the transition from flint to percussion. Gettin' off topic, but thought I'd throw this in.
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