Melville Falkner Rogers, son of Amos Frankford Rogers and Margaret Rebecca Falkner, was born in Ottawa, January 5, 1899 (Ontario birth registrations). Melville's siblings included Frankford Ernest Rogers (born April 20, 1897) and Gladys Margaret Rogers (born June 1, 1903). In Ottawa on March 5, 1927, Melville married Isobel Hossack Blyth, daughter of James Thorp Blyth and Isabella Evans Thomson (Ontario marriage registration). According to that marriage registration, Melville was a lawyer. Melville and Isobel (1904–1968) are buried in the Beechwood Cemetery, section 49, lot 44 (Beechwood Cemetery burial registers).
As a pair skater, he won the silver medal at the 1922 Canadian Championships and the bronze medal at the 1923 Canadian Championships with partner Cecil Smith. During those years, he represented the Toronto Skate Club in competition. He won the 1925 Canadian Championships, the silver medal at the 1928 Championships, and the bronze medal at the 1929 Championships with Gladys Rogers, representing the Minto Skating Club. He won the bronze medal at the 1926 Canadian Championships with partner Isobel Blyth, whom he married in 1927 (Ontario marriage registration 1927 009200).
As an ice dancer, he won the silver medal at the 1940 Canadian Championships with Elmore Davis. They also won the Junior national title that same year.
In the fours discipline, he won the 1922 Canadian fours silver medal with partners Sidney Pepler, Frankford Rogers, and Katherine Capreol. He won the 1929 Canadian fours silver medal with partners Frances Claudet, Katherine Lopdell, and Guy Owen. He won the 1931 Canadian fours bronze medal with the same team as in 1929. He won the 1932 Canadian fours silver medal with partners Elmore Davis, Prudence Holbrook and Guy Owen. He won the 1933, 1934, 1935, 1936, and 1937 Canadian fours title with the same team as in 1932.
Internationally
He competed at the 1924 Winter Olympics as both a single skater and pair skater. He placed 7th in singles, and 7th in pairs with partner Cecil Smith. At those Olympics, Rogers became the first Canadian men's singles skater to compete at the Olympics and was also a member of the first Canadian pairs team to compete at the Olympics.
Following his retirement from competitive skating, he worked as a judge. He served as the president of the Canadian Figure Skating Association for two terms and remained active with the Minto Skating Club for many years.