Flemyng began his career on stage in the 1930s, including West End productions, and made his Broadway debut in 1938 in Spring Meeting (directed by John Gielgud), followed by No Time for Comedy (1939). When England entered the second World War, he enlisted and his service earned him the OBE (Order of the British Empire) in 1944. Resuming his acting career in 1948, he returned to Broadway in The Importance of Being Earnest (netting a 1948 Tony Award for Ousttanding Foreign Company) and continued to appear in Broadway plays through 1957, in addition to the West End and other British theaters.