Ash Flat is a city in Fulton and Sharp counties in the U.S. state of Arkansas with a population of 1,109 in 2021. Ash Flat was establishe…Ash Flat is a city in Fulton and Sharp counties in the U.S. state of Arkansas with a population of 1,109 in 2021. Ash Flat was established in 1856. The community was so named for a grove of ash trees near the original town site.