He attended Trinity College where he graduatd in 1880 with a BA and an LLB. Once his education was completed, Glynn wasted no time seeking out a new life and emigrated to Australia that very same year. He settled in Adelaide where he established his own legal firm.
While in Australia, Glynn became involved in politics. He was president of the South Australian branch of the Irish National League and was involved in the South Australian Land Nationalisation Society. He also supported women's suffrage. He was elected as a member of parliament in 1895.
He rose through the ranks of Australian politics, serving as Attorney General, Minister for External Affairs, and Minister for Home and Territories. He also played a role in drafting the Australian Constitution.
Glynn retired from the political sphere in 1919.
He died on the 28th of October 1931.