Yes, this happens with LED lights. The older bulb lights are just being switched on or off and thus don't flash.
LED lights however are pulsed for a different brightness, so when filmed with a camera which captures discrete frames, these lights can flash because the camera catches them sometimes on and sometimes off, as daan explained. Example: you have one set of lights for driving and braking. When you do not brake, the LEDs are pulsed. This happens so quickly that the human eye can not distinguish the on-off-periods, so you just see a reduced brightness. When you brake and the lights come on, the LEDs are simply being tuned on all the time, so the light appears brighter to the eye.