[2] He held jobs on trans-Atlantic ships while young, studying while at port with Bill West in New York City and with local musician Tommy Webster in Birmingham.
Kinsey led his own ensemble at the Flamingo Club in London through the 1950s, and recorded on more than 80 sessions between 1950 and 1977, including with Tubby Hayes, Bill Le Sage, Ronnie Scott, Johnny Dankworth, Tommy Whittle, Joe Harriott, Lena Horne, Frank Holder, Ella Fitzgerald, Ben Webster, Clark Terry, Harry Edison, Buddy DeFranco, Billie Holiday, Oscar Peterson, and Sarah Vaughan.
In the mid-1980s, he performed regularly with jazz vibraphone player Lennie Best at venues in the London area, including the South Hill Park Cellar Bar in Bracknell.
His Quintet for string quartet and harmonica, "Reflections", has been recorded by Gianluca Littera and the Quartetto Energie Nove.
[6] Kinsey was a member of the Masonic Lodge and Chapter of Asaph 1319 and was presented with his 50 years Certificates for both by Lt Col Stephen Braden PAGSwB on 3 April 2023.