Brakes on a vehicle cannot catch fire themselves.
Because the brake pads, brake rotors, brake drums, brake shoes etc are all made from metal which is non combustible material.
So while the brakes themselves cannot catch fire the overheated brakes are still a fire risk.
The overheating brakes can cause other parts of the vehicle to catch fire.
If brake fluid begins leaking on the hot brakes then it can catch fire.
Although brake fluid does not burn like gasoline or diesel or oil the brake fluid can sometimes catch fire and burn like candle wax or vegetable oil.
Brake fluid is not a big fire risk but it can catch fire.
So be careful with hot brakes.
Brake rotors and brake drums will naturally and normally get hot because the friction that causes the vehicle to stop creates heat.
But brakes should never get overly hot.