Iinuma was born in Toyoshina (now part of Azumino, Nagano Prefecture), and was a graduate of the Imperial Japanese Army flying school at Tokorozawa.
At age 24 he gained fame as the pilot on the Kamikaze (神風号, Kamikaze-go), a Mitsubishi Ki-15 Karigane aircraft, (registration J-BAAI) sponsored by the newspaper Asahi Shimbun.
It became famous on April 9, 1937 as the first Japanese-built aircraft to fly from Japan to Europe, making the flight between Tokyo and London, in time for the coronation of King George VI and Queen Elizabeth.
The flight was the first Fédération Aéronautique Internationale record won by Japanese aviators.
Iinuma was killed in December 1941 at Phnom Penh airfield in French Indochina when, in a daze from hearing the news of the attack on Pearl Harbor by Japanese forces, he accidentally walked into a spinning aircraft propeller.