I dyed a pair of homemade nylon pants with ordinary Rit dye, and it worked reasonably well. The color may be lighter than expected, or a second treatment may be necessary. Probably some eventual fading, too. I suspect tie-dyeing might not give satisfactory results. The obvious thing to do is to try dyeing some small samples.

I think it would be a bit safer to use mineral spirits rather than white gas to thin the silicone, BTW (referring to a different post).