If for whatever reason we all started Kung Fu fighting with kicks that were as fast as lightning, we would all die:
Taken at face value, everyone would die. The forces required to accelerate limbs up to a fraction of the speed of light would give human legs accelerations in the quintillions of gees. These sorts of accelerations don’t exist anywhere in the universe; neutron star surface gravity is a snail’s pace by comparison. Macroscopic objects simply don’t move this fast. I cannot emphasize more strongly how far outside the realm of ‘plausible’ we are.
But let’s be generous. Suppose the human body could withstand these accelerations. What happens when that first kick is thrown?