Which component is responsible for flushing toilets in the aircraft?

The potable water system is responsible for flushing toilets on the aircraft. This system supplies clean drinking water that is also used for various other purposes, including the flushing of lavatory toilets. The aircraft's toilets function using a vacuum system that relies on the potable water system to provide the necessary water for flushing.

The reason the other systems do not apply is that the pneumatic system mainly deals with pressurized air that powers various components of the aircraft but does not provide water. The fuel system manages the aircraft's fuel supply and is unrelated to toilet operations. The water recycling system, while relevant for managing wastewater, is not what directly provides water for flushing toilets. Thus, the potable water system is the correct choice as it is directly involved in supplying the necessary water for toilet flushing onboard the aircraft.