Stout was born in New London, Missouri, in 1879, and attended the University of Missouri at Columbia, where he studied and later taught law. In 1902, he moved to Lewistown, Montana, and entered publishing, working as the editor and publisher of the Fergus County Democrat from 1902 to 1916 and the Lewistown Democrat News from 1916 to 1946.
He was elected to the Montana Senate in 1910, and served until 1913.
Congress
Following the 1910 United States Census, Montana gained an additional seat in the United States House of Representatives. Rather than create separate districts, the existing Montana's at-large congressional district began separately electing two members, and Stout ran for Seat B in 1912. He was narrowly elected to the seat and was re-elected in 1914. Stout did not seek re-election in 1916 and returned to Montana, continuing his work in the newspaper business.