Clancy Mckenna was the son of station manager Morris McKenna from Ireland and grew up on Meentheena Station in the Pilbara. Clancy belonged to the Burungu skin group. His mother belonged to the Banaga skin group and Nyamal people. He was raised by his mother. He was fathered by Frank Djungunbuna who belonged to the Garimara skin group.
Clancy McKenna, Peter Coppin and Don McLeod were central figures in orchestrating the historic strike of Aboriginal pastoral workers in the Pilbara on May 1st 1946. From twenty-seven pastoral stations in Western Australia, Aboriginal workers walked off the job for better pay and conditions.