Flynn was born in Phoenixville, Pennsylvania on February 13, 1861, son of Dennis T. and Margaret (Clancy) Flynn. He moved with his mother to Buffalo, New York, in 1863. There, he became an orphan at the age of three when his mother died. He was raised in a Catholic orphanage where he remained until 1880. He attended common school and then Canisius College in Buffalo. He married Addie M. Blanton in 1887.
After college, Flynn moved to Riverside, Iowa, where he established and edited the Riverside Leader and studied law. He was admitted to the Iowa bar association in 1882 and commenced practice in Kiowa, Kansas. There, he was the publisher of the Kiowa Herald and served as first postmaster of Kiowa from December 5, 1884, to July 17, 1885. He would then serve as the Kiowa city attorney from 1886 to 1889.
Flynn then moved to Oklahoma Territory where he served as the postmaster of Guthrie from April 4, 1889, to December 20, 1892. A Republican, he was an unsuccessful candidate for election as the Territorial Delegate to the United States House of Representatives in 1890. He ran again and was elected as the Territorial Delegate to the Fifty-third Congress and began his term on March 4, 1893 and was reelected in 1894. Flynn was an unsuccessful candidate for reelection in 1896.
Flynn ran for office again in 1898 and was elected to the Fifty-sixth Congress. His term began on March 4, 1899 and he was reelected on 1900. Nominated but declining to be a candidate for reelection in 1902, he left office when his term ended on March 4, 1903. He resumed private practice in Oklahoma City in 1904. He was an unsuccessful Republican candidate for election to the United States Senate in 1908, losing to the Democratic candidate, Thomas P. Gore. He was considered for the position of Secretary of the Interior under President William Howard Taft. He served as a delegate to the Republican National Convention in 1912, his last participation in politics.