He was educated in Swansea at Bishop Gore School, where a teacher, Mr Foukes, encouraged his interest in physics.
[1] Flowers worked on the Anglo-Canadian Atomic Energy Project Tube Alloys at Chalk River, Ontario from 1944 to 1946, then joined the Atomic Energy Research Establishment (AERE) at Harwell, Oxfordshire until 1950 when he moved to the department of Mathematical physics at the University of Birmingham.
[1] Flowers was chair of the Computer Board for Universities and Research Council from 1966 to 1970, member of the Atomic Energy Authority from 1971 to 1981, and president of the Institute of Physics from 1972 to 1974.
Between 1978 and 1981, Flowers was chair of the Commission on Energy and the Environment, between 1979 and 1980, of the University of London Working Party on future of medical and dental teaching resources and between 1983 and 1985, of the Committee of Vice-Chancellors and Principals.
He was also a member of the council of the Academia Europaea from 1988 to 1991, governor of Middlesex University from 1992 to 2001 and chair of the Committee of Enquiry into the Academic Year in 1992 and 1993.