Some years ago I died the silk span on a Barnstormer to see how it would work, I used Rit brand dye, and mixed the dye in thinner, letting the dye settle, then shaking it many times to blend into the thinner.
Then I mixed the thinner into clear dope, about 50/50 and doped the silk span, it turned out okay, but the dye faded in the sun light.
Hope that this helps, and good luck..