At Los Angeles in 1932 Walter Flinsch won a silver medal in the coxless fours and was eliminated in the repêchage of the eights. Four years earlier, he was eliminated in the single sculls in the repêchage. He was German champion in 1923-24 and 1926-28 in the single sculls, 1924 in the double sculls, 1930 in the eights and coxed fours, and 1931 in the eights and coxless fours. Until 1929 Flinsch rowed for Frankfurter RV von 1865, and then joined Mannheim rowing club Amicitia 1876.
Flinsch came from the Frankfurt branch of a paper industrialist family. Before World War II, he was a pilot for Lufthansa and naturally joined the Air Force when war broke out. As a test pilot in 1943, he lost control of his bomber Heinkel He 177 Greif at an altitude of 4,000 m. He was able to leave the aircraft but never had a chance to open his parachute.