Geologist. Born in Kirkwall (Orkney), the son of the merchant, Flett was educated at Kirkwall Burgh School, George Watson's College in Edinburgh, and the University of Edinburgh, where he studied art, science and medicine. He briefly practised in medicine, but soon joined his alma mater to assist Professor James Geikie (1839 - 1915). He taught petrology at the University but also worked for the Geological Survey of Great Britain from 1901, rising to become Assistant Director in 1911 and Director (1920–3). During his first decade with the Geological Survey was an integral part of fieldwork in the Scottish Highlands and in the South West of England. As Director, he moved the Headquarters of the Survey and the Geological Museum in South Kensington (London) and also established regional offices for the Survey around the UK.
Flett was awarded an honorary degree by the University of Edinburgh in 1912, with an OBE in 1918 and was knighted in 1925. He was elected a Fellow of the Royal Society of Edinburgh in 1900, a Fellow of the Royal Society in 1913 and was awarded the Wollaston Medal of the Geological Society of London in 1935.
He died at his home in Essex. A lecture theatre at the South Kensington museums complex was named in his honour in 1976, as were the Flett Crags in Antarctica.