Koolaid works fine on silk, as silk is a protein fiber. Silk doesn't wet very quickly, though, so be sure to pre-soak the scarf well, and it helps if you add a tiny bit of Synthropol or dishwashing liquid to the soaking water.
By "very well," Sheila means as long as over night. What looks wet to your eye isn't necessarily thoroughly wet to the core of the fiber.
Lissa
"Expecting the world to treat you fairly because you are a good person is a little like expecting the bull not to attack you because you are a vegetarian." --Dennis Wholey