What I use isn't an option either: Fiber optics. I have a nice little 3' tree with fiber optic lights built in. They don't exactly 'flash' or 'twinkle', but its more of a wave effect of colors. VERY pretty and rather hypnotic.
I used to use twinkle lights, but the sets that had variable speeds since I can't handle rapid flashes of light either (they give me horrid headaches). I prefer colors, but there's something majestic about the solid white lights when done well. :)