The 1807 and 1814(ish) dates agree with the information I have.
The Rev Alexander John Forsyth was a minister of Belhelvie in Aberdeenshire, Scotland.
It is said that Rev Forsyth was an avid bird hunter and was unhappy with the way birds would change their flight pattern when they saw the flash of the powder in a flintlocks pan. He decided to try using one of the fulmates which had been known for some time, but no practical use for them had been found.
He patented the first percussion system in 1807. This was the "scent bottle" style which deposited a small amount of potassium chlorate into a tube that fit into the breech of the barrel. This tube contained a pin or piston, which when struck by the hammer transfered the impact to the powder causing it to explode.
Following this, many different methods of containing and firing the fulminate was tried.
Around 1814 according to W. W. Greener, the cap method of containing the fulminate was first used by Joshua Shaw of Philadelphia who used a reloadable steel cup for priming. By 1816, he had replaced the steel cup with a copper cap very similar to what is now in use.
By the mid 1820's the percussion cap was becoming common and by 1830, very few flintlock guns were being made for the general population.
To answer the Posts original question, by 1836 the use of percussion caps was common and the Flintlock was considered obsolete by the general population.
As for the U.S. Military's not using the percussion system, their reluctance to use the new system was (is) to be expected. They tended to stick to the "proven" rather than accept new ideas which were commonly used by the general public.
The first U.S. Military gun using the Percussion cap (aside from a few Halls which were not widely issued) was the 1842 Springfield, a .69 caliber smoothbore. This gun was issued to the troops in fairly large numbers and saw use in the Mexican/American war as well as the Civil War.
zonie