The phrase "goes flat-out" is often used to describe someone putting in maximum effort or driving/running at full speed. There are several synonyms that could be used instead, depending on the context and the desired effect. Some options include "gives it their all," "pushes themselves to the limit," "puts the pedal to the metal," "runs at top speed," "exerts themselves to the fullest," "throws themselves into it," "goes all out," or simply "gives everything they've got." Using these synonyms can help add variety to your writing and better convey the intensity and dedication that someone is putting into a particular activity.