He is the father of Thomas Flögel. Rudi Flögel played almost his entire career at Rapid Wien, where he captained the team in his last two seasons before moving to Admira Wiener Neustadt and Simmering. He made his debut for Austria in a May 1960 friendly match against Scotland.
He earned 40 caps, scoring 6 goals.
His last international was a September 1969 friendly match against West Germany.