Kincaid served as a Kentucky Commonwealth attorney. He was also a member of the Kentucky House of Representatives in 1819. He was elected as a Jacksonian to the Twenty-first Congress (March 4, 1829 – March 3, 1831).
Kincaid served as the chief prosecutor for the state of Kentucky. In addition, he represented his home state in the Kentucky House of Representatives in 1819. He was later elected to the Twenty-first Congress as a Jacksonian (March 4, 1829 – March 3, 1831).