The phrase "flies the handle" is a somewhat obscure way of saying that someone has lost control or gone berserk. If you're looking for a more common alternative, "loses their cool" or "flies off the handle" are both phrases that convey a similar idea. Other synonyms might include "has a meltdown," "goes haywire," "flips out," or "blows a gasket." More formal phrases might include "experiences a breakdown" or "suffers an emotional outburst." Regardless of the specific wording, the underlying sentiment is the same - someone has lost their grip on reality, their temper, or both.