The influence of centrifugal acceleration on the form and stability of the Bunsen burner stabilized flame is studied. It is shown that as the angular velocity of rotation increases, the classical Bunsen cone first slightly buckles at the tip. Buckling then becomes more prominent, and eventually the flame enters the burner. At sufficiently rapid rotation, flame stabilization by the burner rim becomes impossible and the flame flashes back. The theoretical findings are in favorable agreement with the experimental observations made on a rotating Bunsen burner.