Do sailors use flags when the radios are broken?

Answer 1

They could, using semaphore flags or signal flags.

But there are other reasons to use the flags rather than broken radios. The best reason is when maintaining radio silence. The enemy can't intercept flag signals unless they are in visual range. And they can't locate the ships using radio tracking devices.

Directional flashing light is considered even more secure.

Flags are also used to indicate certain situations on board the ship that would not normally be sent over radio signals. The most common is flying the Bravo flag while handling ammunition or fuel. Each ship also has a unique flag name that is typically flown to identify it to other ships when they are too far away to read the numbers or sides.

Entire messages can be coded and flown using various code books. Often fleet maneuvers are signaled using flags.

And the international signals can be used to communicate across languages. Each ship has the same international code book in its own language. It is very good for signaling when there is an emergency and help is needed and there are not translators available.