Born in Valleyfield, Fife, Kelly began his career with Perth-based junior club Jeanfield Swifts.
He joined English club Blackpool in 1943 as a 20-year-old, but due to the ongoing World War II, he didn't make his League debut for the Seasiders until September 1946.
However, in the final home league game of the 1952–53 season against Liverpool he suffered a broken ankle following a tackle by centre-forward Louis Bimpson and he missed the famous 1953 match-up with Bolton Wanderers, although the club asked the Football Association to produce a special winners' medal for his nomination as "twelfth man".
"[2] The 1950s was the most successful decade in Blackpool's history to date, and Kelly was at the club playing top division football throughout, as were goalkeeper George Farm, defender Tommy Garrett, right winger Stanley Matthews, forward Jackie Mudie and outside left Bill Perry.
[2][4] His funeral was held at Sacred Heart Roman Catholic Church, Blackpool, and he was cremated at Carleton Crematorium.