He served with the New Zealand Army New Zealand Expeditionary Force as an under-age private in France before being appointed as an official War Artist during World War I. After the war, he studied at the Regent Street Polytechnic School of Art in London and arrived in Sydney in 1919. In 1921 he was appointed by Alex Sass as a staff artist with Smith's Weekly.
Although he started with humorous sketches, it was for his caricatures that he became famous, initiating in Smith's Weekly a "Man of he Week". The first subject was Archbishop Mannix. He was sacked by Smith's Weekly after a legal tussle over ownership of works he had produced for the paper.
He worked for the Labor Daily for three months before being dropped for his antagonism towards Jack Lang, then with Truth for a few years. He also worked for the Daily Telegraph, which he left in 1945 after Will Mahony had refused to draw an anti-Labor cartoon, and the Militant Minority Movement paper The Red Leader.
Finey also illustrated stories and articles appearing in the School Magazine published by the NSW Department of Education. The issues of June and August and Sept 1947 contain examples of his work.
He then turned to painting in an expressionistic style; possibly the first Australian painter to experiment with collage.
"Money for paints is scarce if you are living on the pension, and Finey creates constantly out of waste, scrap and natural materials. He has made a whole series out of rolled-up, varnished newspapers, and he is adding to his History of Music with portraits of composers done in plastic foam, etched out with fine sandpaper. He uses rags, twine, shells, clay and stumps taken from the bush..."
He was considered by Stan Cross to be the greatest of Australia's newspaper artists. George Blaikie remembers him as an unkempt long-haired sandal-wearing bohemian, fearlessly honest in his work, and generous to a fault.
- Bathurst Prize for watercolour 1959
- Lindesay, Vane The Inked-In Image Heinemann, Melbourne 1970 ISBN 0-09-135460-9
- "Last of the Great Bohemians" by Margaret Jones. Sydney Morning Herald, Weekend Magazine, Saturday June 13, 1970.
- Blaikie, George Remember Smith's Weekly Angus & Robertson, London 1967
- Art in Australia issue June 1924
- Art in Australia issue June 1931