According to the United States Census Bureau, the village has a total area of 7.9 square miles (20.6 km²), of which, 7.8 square miles (20.3 km²) of it is land and 0.1 square miles (0.3 km²) of it (1.26%) is water.
The elevation of Flat Rock is 2,207 ft.
There were 1,169 households out of which 15.3% had children under the age of 18 living with them, 76.5% were married couples living together, 1.8% had a female householder with no husband present, and 19.8% were non-families. 18.0% of all households were made up of individuals and 10.9% had someone living alone who was 65 years of age or older. The average household size was 2.19 and the average family size was 2.46.
In the village the population was spread out with 13.6% under the age of 18, 2.3% from 18 to 24, 13.4% from 25 to 44, 34.9% from 45 to 64, and 35.8% who were 65 years of age or older. The median age was 58 years. For every 100 females there were 99.3 males. For every 100 females age 18 and over, there were 95.0 males.
The median income for a household in the village was $67,813, and the median income for a family was $81,811. Males had a median income of $55,263 versus $34,375 for females. The per capita income for the village was $42,222. About 0.3% of families and 1.5% of the population were below the poverty line, including none of those under age 18 and 2.5% of those age 65 or over.