His father was awarded the Military Cross for going back to the burning tank for medication for his men, making his injuries worse.
Mr Jennings had thought his life was over, but after surgery became a teacher and a headmaster, and had 11 children, the Daily Mail reported.
Mr Jennings is the sculptor of Sir John Betjeman in London's St Pancras Station.
The men helped by Sir Archibald's experimental treatments formed the Guinea Pig Club, which held an annual meeting for more than six decades to honour the work of the man who died in 1960.
Sir Archibald was born in Dunedin on May 4, 1900, the second of four children. He attended Otago Boys' High School, and studied at Otago Medical School.
In a feature about Sir Archibald and the Guinea Pig Club in the Otago Daily Times in 2006, Barry Cardno wrote that Sir Archibald was noted early in his career for his quick cool judgement.
He moved to London in 1930, from the United States where he studied surgery at the Mayo Clinic.
In England, he contacted a distant relative, Dunedin-born Sir Harold Gillies, who is considered the father of 20th century plastic surgery. Sir Harold was knighted in 1930, for his work treating the injuries caused by shrapnel and bullets in WW1.
Sir Harold taught Sir Archibald the skills of the burgeoning specialty, which the younger man would advance through pioneering new techniques.
Sir Harold was appointed principal plastic surgeon for the army at the outbreak of WW2, and Sir Archibald was sent to East Grinstead to establish a unit providing specialist treatment for a new form of injury affecting airmen, known as "Hurricane Burn".
He developed a new way of treating serious flesh burn, keeping the skin moist so it could be peeled back to make way for skin grafts.
He understood the psychological effects of such injuries, and kept the men's spirits high.
Last year, Otago Boys' High School announced it was establishing a house system for the first time. One of the four new houses, McIndoe, is named for the illustrious old boy.