Kelly joined the civil service as a messenger boy at the age of 15. While working at the Office of National Education he met Tom Collins, a wit with a talent for light verse. The pair joined the Mount Argus Players amateur dramatic society, where they met Arthur Booth. After the Mount Argus Players disbanded, Kelly and Booth joined the Rathgar Players, and, discovering a shared passion for cartooning, decided to launch their own humorous magazine. Collins was recruited as a writer.
The magazine was to be called Dublin Topics, until Kelly persuaded the others to rename it Dublin Opinion. Booth was its first editor, and drew the covers. The first issue, funded by a loan from a friend of Booth, launched on 1 March 1922. 3,000 copies were printed, and sold out, but the second issue sold poorly. From issue 3 it was distributed by Easons, and within four years was selling 40,000 copies a month. After Booth's death from pneumonia in 1926, Kelly, Collins and Booth's father-in-law Major Robert J. Baker formed Dublin Opinion Ltd, Collins and Kelly took over as editors, and Kelly became chief artist. His prolific contributions to the magazine were drawn in a variety of styles, from cartoony to illustrative. He had no formal art training, and developed his style by studying the work of the leading cartoonists of the time. From a peak of 60,000 copies a month, sales began to decline in the mid 1960s. Kelly and Collins wound the magazine up in 1967, and sold it to Louis O'Sullivan in 1968.
Kelly continued to work in the civil service, eventually becoming Director of Broadcasting and Director of National Savings. His cartoons were also published in The Capuchin Annual from 1942 to 1955. He began painting watercolours in the 1930s, and became a member of the Dublin Sketching Club and the Water Colour Society of Ireland: he exhibited over 60 pieces at the latter from 1941 to 1980, and had a solo exhibition of his watercolours in Dublin in 1972. He received an honorary doctorate from the National University in 1979, and was president and chairman of PEN.
His first wife died in 1965. They had three daughters, including the journalist Pauline Bracken, whose memoir, Light of Other Days: A Dublin Childhood, was published in 1992, and three sons, including the actor Frank Kelly, best known for playing Father Jack in the Channel 4 sitcom Father Ted. He married his second wife, Peggy Nelson, in 1972. He died in 1981 after a long illness.
- Thomas J. Collins & Charles E. Kelly (eds.), Fifteen Years of Dublin Opinion, Dublin Opinion Ltd, 1937
- Louis McRedmond (ed.), Modern Irish Lives: Dictionary of 20th Century Biography, Gill & McMillan, 1998, p. 154
- Theo Snoddy, Dictionary of Irish Artists: 20th Century, Merlin Publishing, 2002
- Frank Kelly, "The Story of Dublin Opinion", The Political Cartoon Society
- Interview with Frank Kelly, Sunday Mirror, 14 March 1999
- Anne Dolan, "Kelly, Charles Edward"; Pauric J. Dempsey and Bridget Hourican, "Booth, Arthur James Conry"; Anne Dolan, "Collins, Thomas Joseph", Dictionary of Irish Biography, (Eds.) James Mcguire, James Quinn, Cambridge University Press, 2009