Glynn was the son of John McMahon Glynn of Gort, County Galway. Educated at Blackrock College, he became a solicitor in 1890. Nine years later he was elected to Galway County Council and acted as its chairman from 1902 to 1912.
He was knighted in 1915 while Chairman of the National Insurance Commissioners. While President of the Irish Council of St. Vincent de Paul, he was admitted to the Order of St. Gregory the Great. He was also a leading member of An Ríoghacht.
- Knockmoy Abbey, in Journal of the Royal Society of Antiquaries, xxiv, 1904
- Life of Matt Talbot, Catholic Truth Society, Dublin, 1927
- Beatha Mhartin Talboid 1856–1927, 1935
- Galway Authors, Helen Mahar, 1976
- Maurice Curtis, A Challenge to Democracy: Militant Catholicism in Modern Ireland, The History Press Ireland, 2010, p. 55