Martin Flämig studied since 1934 in Dresden with Alfred Stier and in Leipzig at the Kirchenmusikalisches Institut des Leipziger Konservatoriums with Karl Straube, Günther Ramin, and Johann Nepomuk David. He was since 1948 cantor at the Versöhnungskirche in Dresden and premiered there Willy Burkhard's oratorio Das Gesicht des Jesaja (The Vision of Isaiah), Ernst Krenek's Lamentationes Jeremiae Prophetae and Johannes Drießler's Dein Reich komme.
In 1953 he was appointed professor of the Hochschule für Musik Dresden. He was a teacher at the Bern Conservatory since 1959. In 1971 he was appointed Dresdner Kreuzkantor as the successor of Rudolf Mauersberger and held the post until 1991.