I found the best method was to simply paint the colors right on the floss with a thin brush. I also found that it really helped to hold the floss taut and in place. I used tape for this.
I painted one side then flipped it over and did the other side and also filled in any little remaining blank spaces that needed it. This took several days since drying time for each color was needed.
After it was done I un-taped it all, put it in a
small pouch and tossed it in a dryer for about
20 minutes or so to set the colors.
I was happy with the result. I get a different color for almost every stitch, and as a bonus many of the stitches have multiple colors in them - some with different colors on each end or sometimes split horizontally down the middle.
I used this 'homemade painters floss' with this piece and this one.
Hopefully this is just the beginning.....