Recent empirical data for short-burst lift and power production of flying animals indicate that mass-specific lift and power output scale independently (lift) or slightly positively (power) with increasing size. These results contradict previous theory, as well as simple observation, which argues for degradation of flight performance with increasing size. Here, empirical measures of lift and power during short-burst exertion are combined with empirically based estimates of maximum muscle power output in order to predict how burst and sustainable performance scale with body size. The resulting model is used to estimate performance of the largest extant flying birds and insects, along with the largest flying animals known from fossils. These estimates indicate that burst flight performance capacities of even the largest extinct fliers (estimated mass 250 kg) would allow takeoff from the ground; however, limitations on sustainable power output should constrain capacity for continuous flight at body sizes exceeding 0.003-1.0 kg, depending on relative wing length and flight muscle mass.