Miller attended classes at University of Michigan, and then studied law independently. He began a private practice in Owensboro, Kentucky in 1916. He entered the United States Army in 1918, and resumed his practice the same year in Owensboro, until 1945.
While maintaining his private practice, Miller also served as county attorney in Daviess County, Kentucky from 1921 until 1929, and as a member of the Public Service Commission of Kentucky from 1934 until 1935. He served as a judge on the Special Court of Appeals of Kentucky from 1940 until 1941.
Miller was nominated by President Harry S Truman to serve on the D.C. Circuit Court of Appeals on September 12, 1945, to a seat vacated by Fred M. Vinson. Miller was confirmed by the United States Senate on September 24, 1945, and received his judicial commission on September 28, 1945. Miller then served as chief judge from 1960 until 1962, and assumed senior status on October 15, 1964. He remained on the court until his death on January 24, 1976.