Born in Prince Albert on November 12, 1921, Fleming began his musical studies in Saskatoon. In 1937, he traveled to England, studying at the Royal College of Music with Arthur Benjamin (piano) and Herbert Howells (composition). Returning to Saskatchewan, he gave his debut concert at Darke Hall, Regina (1940), followed by a recital tour of the province. He continued piano studies with Lyell Gustin in Saskatoon and later, on Canadian Performing Rights Society scholarships, studied at the Toronto Conservatory of Music with such national luminaries as Healey Willan (composition). In 1946 he joined the National Film Board of Canada, eventually becoming music director (1958). He remained there until 1970, when he took a position at Carleton University, Ottawa, lecturing on Canadian composers and 20th century music.
Robert Fleming was well known for his many compositions encompassing not only hundreds of film scores but a large body of musical works for orchestra, chamber ensemble, solo instrument, voice, choir, ballet, theatre and liturgical music for the Anglican church. The Confession Stone (1967), his internationally known song cycle, shows Fleming's dedication to fine craftsmanship and detailed attention to text. Throughout his career, he had an ongoing influence on many young musicians, and to this day his melodic pieces are regularly heard at the Saskatchewan Music Festival. Fleming died on November 28, 1976.