fleming county is a county located in the state of kentucky. as of the 2010 census, the population was 14,348. its county seat is flemingsburg. the county was formed in 1798 and named for colonel john fleming, an indian-fighter and early settler. it's a prohibition or dry county, which means drinks with alcohol are not sold there. in 1998, the kentucky general assembly designated fleming county as the covered bridge capital of kentucky.