He was born near Danville, Kentucky, where he attended the public schools.
He studied law, was admitted to the bar and commenced practice in Stanford, Kentucky.
After leaving Congress, he was again a member of the Kentucky House of Representatives in 1836 and 1837.
He served as circuit judge in 1836 and 1837 and then resumed the practice of law and also engaged in agricultural pursuits, He moved to Gallatin, Tennessee, in 1870 and died there on February 7, 1873.
Kincaid was buried in Bellevue Cemetery, Danville, Kentucky.