He was born at Meanwood in Yorkshire, and educated at Leeds Grammar School and Pembroke College, Oxford. He worked from 1929 as Deputy Keeper of Manuscripts in the British Museum and, completing the work of Standish Hayes O'Grady, compiled a catalogue of the Irish manuscripts there.

He wrote several collections of poetry, translations of the Irish poets for the Cuala Press, and verses on Blasket Island. He first visited Blasket in 1910, at the recommendation of Carl Marstrander, his teacher at the School of Irish Learning in Dublin; he acquired there the Irish nickname Bláithín. The Blasket Islands on the Southwest Coast of Ireland: Historical information He suggested a Norse origin for the name "Blasket". Under Flower's influence, George Derwent Thomson and Kenneth Hurlstone Jackson made scholarly visits to Blasket.

After his death his ashes were scattered on the Blasket Islands.

As a scholar of Anglo-Saxon, he wrote on the Exeter Book He identified interpolations in the Old English Bede, by Laurence Nowell. His work on Nowell included the discovery in 1934, in Nowell's transcription, of the poem Seasons for Fasting.

He translated from the writings of Tomás Ó Criomhthain, his teacher on Blasket in Irish, and wrote a memoir, The Western Island; Or, the Great Blasket (1944), illustrated by his wife Ida. The essay collection The Irish Tradition (1947) is often cited, and was reprinted in 1994; it includes "Ireland and Medieval Europe", his John Rh?s Memorial Lecture from 1927.