The term 'Flying Cloud of Old Autodom' refers to the REO Motor Car Company, an American manufacturer of automobiles, trucks, buses, and military vehicles founded in 1905 by Ransom E. Olds. The company's most popular model was the REO Flying Cloud, a luxury car produced from 1949 to 1957. The Flying Cloud was known for its stylish design and powerful engine, making it one of the most sought-after cars of its time.