Flint was born at Greenburn, Sibbaldbie near Applegarth in Dumfriesshire on 14 March 1838, the son of Grace Johnston (née Paterson) and Robert Flint, a farm overseer. His first school was at Evan Water then he moved to Moffat. In 1852, he entered the University of Glasgow where he distinguished himself (without graduating) in arts and divinity.
Having been employed as a lay missionary by the 'Elders' Association of Glasgow', Flint was licensed to preach as a Church of Scotland minister by the Presbytery of Glasgow in June 1858, and for a short time acted as assistant to Norman Macleod, at the Barony Church, Glasgow. He was minister of the East Church, Aberdeen from 1859 to 1862, and of Kilconquhar church in Fife from 1862 to 1864, a small country village parish, which gave him leisure for study, improved by visits to Germany.
On the death of James Frederick Ferrier in 1864, Flint was elected to succeed him in the moral philosophy chair at the University of St Andrews, among the competing candidates being Thomas Hill Green. This chair he held till 1876, when he succeeded Thomas Jackson Crawford in the divinity chair of the University of Edinburgh. On this appointment he was awarded doctorates by both the University of Glasgow (LLD) and the University of Edinburgh (DD). Thomas Chalmers had similarly migrated from the one chair to the other.
Flint was appointed to a number of foundation lectureships. He was Baird lecturer (1876-7); in 1880 he travelled to America, and delivered a course as Stone lecturer at Princeton University; in 1887-8 he was Croall lecturer. He was elected on 21 May 1883 corresponding member of the Institute of France (Académie des sciences morales et politiques), and was elected a Fellow of the Royal Society of Edinburgh in 1880. His proposers were Sir Robert Christison, Sir Alexander Grant, Alexander Campbell Fraser and Peter Guthrie Tait. He served as Vice President to the Society for three sessions: 1886–1892; 1893–1899; and 1902–1907.
He resigned his chair in 1903 to devote himself to literary work, a purpose hampered by failing health. His post was filled by Rev Prof William Paterson Paterson (later Moderator of the General Assembly of the Church of Scotland.
- Christ's Kingdom upon Earth (1865) sermons
- Philosophy of History in France and Germany (1874)
- Theism (1877) Baird Lectures 1876/7; 7th edition, revised (1889)
- Anti-Theistic Theories (1879) Baird Lectures 1876/7
- Vico (1884)
- Historical Philosophy in France (1894)
- Socialism (1894)
- Sermons and Addresses (1899)
- Agnosticism (1903)
- Philosophy as scientia scientarum (1904)
- Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783 – 2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X.
- Sell, Alan P. F. (23 September 2004). "Flint, Robert (1838–1910), philosopher and theologian". Oxford Dictionary of National Biography. Vol. 1 (online ed.). Oxford University Press. doi:10.1093/ref:odnb/33180. (Subscription or UK public library membership required.)
- Fasti Ecclesiastaie Scotia p.384
- Gordon 1912.
- "William Paterson Paterson". The Gifford Lectures. Retrieved 10 February 2018.
- "21212 - The Wizard in the Kitching". Bite Magazine. 2015. Retrieved 25 July 2015.
- "Professor Robert Flint, 1838 - 1910. Professor of Divinity at Edinburgh University". National Galleries of Scotland. Retrieved 23 July 2018.
- "Review of Agnosticism by Robert Flint". The Athenaeum (3938): 489–490. 18 April 1903.