“Flat out” is to do something at full effort and not leave anything behind. Athletes apply it to short bursts or final spurts in a race. It is to utilize all the energy you have, no matter how tough it is.
The final 200 meters of the 5K run, the hard effort at the finish of criterium racing, and the climbing of hills during the triathlon take strong muscles but also mental strength. Timing is also critical—so you do not burn out prematurely. You must do short and intense workouts to acquire the ability to generate speed and becoming accustomed to large quantities of lactic acid to prepare for these intense attempts.