Clay first entered national politics riding a wave of nationalist sentiment as a Republican War-Hawk prior to the War of 1812 where he became a young leader of the movement along with John C Calhoun (yes that Calhoun). Clay was not a Federalist, besides the rather important fact that Federalists tended to be pretty divided on the American system and Clay didn't become a fierce advocate for the system until after the war, Clay also lived in a western state with a minuscule federalist presence. Moreover Clay represented the West and western interests just as much as Jackson would two decades later and Federalists tended to oppose the development of the west. Probably most importantly though Clay's early views on the future of America were more aligned with Jeffersonian thought.

In short it would have been politically stupid for him to be a federalist, his position was more aligned with Republicans anyway, and by the time of the American system Federalists were divided on the economic aspects anyway