The copper percussion cap was invented in the 1820's. Lewis Winant, in "Early Percussion Firearms" indicates that quite a number of different people claimed to have invented it.
J&S Hawken were in business in St Louis by 1825, per Charles E. Hanson, Jr. in "The Hawken Rifle: its Place in History" Same source: The first documented Hawkin RIFLE was made in 1831. By 1831--32 at least some of these rifles were percussion. Peak production was in the Gold Rush years.
I believe there is no, or in1979 was no, documented J&S Hawken flint rifle.