Kladis started racing in midget cars in 1935. He stopped racing in the 1940s when all racing in the United States stopped for World War II. During the war, he was a pilot in the United States Army. After the war, he started in the 1946 Indianapolis 500 for Andy Granatelli and finished 21st. He drove 50 laps as a relief driver for Spider Webb in the 1954 Indianapolis 500. Kladis attempted to make the field until the 1957 Indianapolis 500 but was unsuccessful.