Viscose can be dyed but in my experience it doesn’t take up the dye nearly as well as cotton, silk or linen. The other issue is that for best results you have to get the dye mix very hot and keep it hot for a while (say, half an hour). Cotton can usually handle that but viscose sometimes shrinks. Viscose usually doesn’t like being soaked.
What are the washing instructions on your jumpsuit? Does it say cold wash only? If so, there might be a shrinkage issue with hot water.
But… if you are going to discard the jumpsuit otherwise, it might be worth a try in any case. I’d just try a low key “soaking” version and see how you go. Get a bucket of hot water, put it in the laundry, add salt* and dye and then put your jumpsuit in it. Agitate the mixture every 5-10 minutes to avoid splotches. I’d use RIT liquid dye. At least one whole bottle. The more you use the more saturated the result. Leave it in there as long as you can. (It doesn’t matter that the water eventually goes cold, the first 15 minutes is the critical part.)
*It might be better to use vinegar (rather than salt) on viscose. The instructions on the bottle will give you the best advice.
