Flat white would be the ultimate "stipple". The reason a smooth parabolic reflector has lots of throw is that (in an idealized model) the shape takes all the light as it diverges from the filament and sends it all out in parallel rays. It's simply a function of the geometrical shape. As you begin adding roughness to the surface of the reflector, some of those rays that would have been parallel, end up going off in other directions. Thus, "throw" is reduced and "spill" increased and the hot-spot widens. You have introduced a certain amount of randomness to the otherwise "perfect" geometric shape.
A flat-white surface would have the most randomness, as light striking it would have a tendency to be scattered completely at random. That is the definition of "flat", as opposed to glossy or semi-glossy where a given portion of the light will be reflected in accordance with the angle of incidence. I.e, light hitting a glossy, white surface at 45 degrees will largely be reflected at 45 degrees. Light hitting a glossless white surface will be reflected in all directions.
I would expect a smooth reflector coated with flat white paint would project a beam that pretty much be the same intensity from edge to edge* -- and those edges would be the same as the normal "spill" width of the flashlight. Of course, nothing's perfect and your "flat" paint would probably have at least a little bit of "gloss". That is, it would still have some slight tendency to reflect at the angle of incidence.
*Edit - actually now that I think about it, there would be somewhat a falloff of intensity at the edges. Look at it as if you are the wall, and how much of the reflector you can "see" from any particular spot. Near the edges, you won't be able to see all of the reflector so the intensity will be somewhat less. however, the intensity per square inch of the visible portion of the reflector should be fairly the same regardless of where you stand. This is different than a metallized reflector where there is a big difference in the apparent intensity of the reflector depending on where you stand.