Glynn was educated at Solihull School and studied at Cambridge, qualifying as a doctor in 1989. He trained in both anaesthesia and emergency medicine before being appointed as a consultant anaesthetist to the NHS. Within the military, regular service was followed by reserve service which culminated in Command of a Field Hospital, both in the UK and in Afghanistan.

Glynn retired from the Army in 2019. He cooks better than most people expect, is an armchair follower of international rugby and a devotee of the works of the late Sir Terry Pratchett.