Dunn was born on 23 February 1915 in Bloxwich, Staffordshire (now West Midlands). His father was victimised after the General Strike for a long period and and then found work in the Kent coalfields.
Jack followed his father into the pits, working at Snowdown, Tilmanstone and Betteshanger. He was elected as a Communist councillor for Deal in the immediate post-war period. Later, he held many positions in Kent Area NUM, including its member of the national executive.
He was most well-known for being the full time Area Secretary of Kent NUM for many years and was the Chair of the South-East Region of the TUC in the 1970s.
A firm supporter of the Morning Star in the 1980s internal conflicts of the Communist Party, he died on the 14 March 2002.