Flat Rock is an unincorporated community in Washington Township, Shelby County, in the U.S. state of Indiana.Flat Rock was platted in 1855. The community took its name from the Flatrock River. The post office at Flat Rock has been in operation since 1828.Flat Rock had its own high school at the turn of the 20th century.Flat Rock is located at 39°21′51″N 85°49′54″W / 39.36417°N 85.83167°W / 39.36417; -85.83167.