Flexmore Hudson was educated at Adelaide High School and graduated from the University of Adelaide. He began a teaching career in 1934 and taught in the Mallee, and at Scotch College in Adelaide and Adelaide Boys' High School.
During the period 1941 to 1947, while he was a schoolteacher at Hammond in the north of South Australia, Hudson founded, edited and published the literary journal, Poetry, at a time when there were few opportunities for publication of Australian verse. He also edited the 1943 anthology of Australian verse for Jindyworobak and contributed to the Jindyworobak anthologies from 1938 to 1953. His writing, including critical articles, short stories, poetry and radio plays for children, was widely published in Australia, New Zealand, England, France and the USA. In 1946 Hudson was awarded a Commonwealth Literary Fund Grant and he was an active member of the Fellowship of Australian Writers and the Melbourne Bread and Cheese Club.