Fleming was born in Glasgow and studied at the Glasgow School of Art. He began printmaking at art school, and Glasgow Art Gallery bought two of his prints while he was still a student. In 1928, Fleming made his first engraving while working with Charles Murray, and he soon became a highly-skilled engraver. While lecturing at the Art School from 1931, Fleming met William Wilson, the Edinburgh-based printmaker and stained glass artist. They became friends, and their work was mutually influential. He also taught Robert Colquhoun and Robert MacBryde during this time and later became Head of Gray’s School of Art in Aberdeen. Fleming produced detailed etchings and engravings of Glasgow, the Scottish Highlands and the Continent.