It doesn't matter what kind of light you use, but it has to be tightly controlled, so flash is much easier.
The trick is to control the direction of incidence, and therefore the direction of reflectance. It's easier if it's just lying flat because when it's on a model or a mannequin it will be crumpled as in your example shot, and light will reflect at all sort of unwanted angles... - so take the time you need to get it really flat.
Get the largest, most diffused light source you can (large softbox is ideal, place it at something like a 45 degree angle to the subject so that the light reflected from the reflective strips exits at an angle that goes nowhere near the lens. Put either a very similar softbox or a large white reflector in the opposite position so that it's lit from both sides.