What kind of dye do I use on wrapping thread

Why dye wrapping thread? Just buy the color you want.
Norm

If you are asking about coloring short lengths of thread for inlaid turns you should think about India Ink pens in the desired color.

I'm looking to dye a spool of thread

Thread comes in a wide variety of colors. Buy the shade or color you want.

..........

you'll never be able to do it, the thread is too tightly wound and the dye will not permeate into the core of the spool.

Dennis J. Danku
(Sayreville,NJ)

Thread is dyed under huge pressure for long periods of time. If you insist on trying it I would leave the thread in the dye for DAYS.

Many builders use, in addition to the "rod builder" thread sources, Madeira embroidery thread with good success. It's hard to believe that you cannot find your color in there. There is nothing you can do at home that will work as well. You will have to use CP.

X-2 with Dennis - Maderia or Sulky (available in the Northeast at JO - Anns or other fabric shops) is
labeled as poleyneon(Maderia) or something close to it. You will also find Rayon on the shelves - totally
unsuitable as it does not like our finish materials. The problems with embroidery threads are the spool
size and they are lubricated to allow them to glide through automated machines. The lubricants they use
do not like our finishes at all. As Michael said, CP is needed before finish or it will probably be rejected
If you want Maderia contact Billy Vivona - Nerbs (sponsor on left). He has a full range of colors as well as
expert advise on color choices etc.