Slack was born on 22 April 1937 in Ashton-under-Lyne, Lancashire, England; the first and only child of Albert and Eva Slack. He studied biochemistry at the University of Nottingham, where he graduated with a Bachelor of Science (Honours) in 1958, and a PhD in 1962. He married Pam Shaw in March 1963, and had two children.
From 1962, Slack worked as a biochemist at the David North Plant Research Centre in Brisbane, Queensland, Australia (funded by the Colonial Sugar Refining Co. Ltd). In 1970, he joined the Department of Scientific and Industrial Research in New Zealand. From 1989 until his retirement in 2000, Slack was a senior scientist at the newly formed Crown Research Institute for Crop & Food Research in Palmerston North.
Slack died in Palmerston North in 2016.