Born in Wake County, North Carolina near Raleigh, Dunn was the son of Grey and Lydia Baucum Dunn. He moved with his father to Limestone County, Alabama, in 1837. He attended the country schools, and was graduated from Jackson College, Columbia, Tennessee, in 1854. He studied law, and moved to St. Francis County, Arkansas, in 1856. He married a Ms. Ellenora (also spelled Ellanora) Patton. Later, he remarried to another Arkansas resident, Anna Fussell, with whom he had two daughters, Anna Mae Estes Dunn and Dorothea Dunn who died as an infant in 1888.
