It depends on your state, but I think most states restrict the use of a constant blinking light (in certain colors like red and blue) to authorized emergency vehicles.
Googling the Wisconsin Vehicle code, I found this:
347.07 Special restrictions on lamps and the use
thereof. (1) Whenever a motor vehicle equipped with headlamps
also is equipped with any adverse weather lamps, spotlamps
or auxiliary lamps, or with any other lamp on the front
thereof projecting a beam of intensity greater than 300 candlepower,
not more than a total of 4 of any such lamps or combinations
thereof on the front of the vehicle shall be lighted at any one
time when such vehicle is upon a highway.
(2) Except as otherwise expressly authorized or required by
this chapter, no person shall operate any vehicle or equipment on
a highway which has displayed thereon:
(a) Any color of light other than white or amber visible from
directly in front; or
(b) Any color of light other than red on the rear; or
(c) Any flashing light.
347.145 Deceleration warning lights for motorcycles,
motor bicycles, mopeds or motor buses. (1) A motorcycle,
motor bicycle or moped may be equipped with and use a
system in which an amber light which pulses in a controlled fashion
at a rate which varies exponentially with deceleration is center
mounted on the rear of the vehicle.
So there you go - no flashing lights allowed, but an amber (which makes no sense since brake lights have to be red) auxiliary flashing brake light is acceptable.
In reality, the application of laws such as these ends up at the discretion of a police officer if you get stopped. They might not even know all the details of the above code but you would be in violation if you used one of those flashing LEDs.
