He became intrigued with jazz in the early 1930s when he was just 12 years old, doing odd jobs at resorts in central Minnesota. His parents and their friends would get together to listen to 78 rpm discs, and Leigh began to appreciate the music. By the end of his teenage years, Kamman was fully in love with the art form. He worked for his school newspaper and found a way to meet Duke Ellington at a train station in Saint Paul when he was just 17 years old.
Kamman's first jazz broadcast occurred in 1940 from WMIN radio where he had been working as a custodian. He moved to WEBC in Duluth, Minnesota in 1942, but didn't really become comfortable with the medium of radio until he found work with the U.S. Army during World War II, broadcasting from KOA in Denver, Colorado with shows that were carried on Armed Forces Radio. Pleased with the impact his broadcasts had on the morale of soldiers, he committed himself to continuing in the field of radio.
He returned to the Twin Cities following the war, coming to work at WLOL. However, he went on to New York in 1950, where he interviewed some of the biggest names in jazz from the Apollo Theater. Kamman returned to WLOL in 1956 and went on to work at KSTP-AM 1500 AM for many years until moving on to MPR. On Sundays, the KSTP shows would link up with other NBC stations around the country, to share the music that was being played in different communities.