The library at the University of Calgary holds a substantial amount of his papers, manuscripts, and transcripts in its "Richard Johnston Canadian Music Archives Collection".
His original fieldwork tapes and transcripts made during his research as a folklorist are part of the collection at the Canadian Museum of Civilization.
He briefly taught on the music faculty of Luther College in Wahoo, Nebraska before beginning private studies with Nadia Boulanger in Madison, Wisconsin in 1943–1944.
During the late 1940s through the 1960s, Johnston worked periodically for the Canadian Broadcasting Corporation as a composer, arranger, conductor, and commentator.
On 12 October 1949 he conducted the chorus for the Canadian premiere of Benjamin Britten's Peter Grimes for the opening of the CBC Opera Company's second season with William Morton in the title role, Edmund Hockridge as Captain Balstrode, Frances James as Ellen Orford, Eric Tredwell as Swallow, and Gordon Wry as Bob Boles.
He was a commentator for the CBC Wednesday Night program Vienna, the Glorious Age (1951) and the radio series Folk Music, A Living Canadian Art (1958).
The Ensemble Vocal Katimavik recorded his arrangement of the Canadian folk song J'ai cueilli la belle rose.
In 1973 he was editor-in-chief of the Western Board of Music piano series Horizons and in 1977 he became the Alberta Composers' Association's first president.