When I do any sort of fabric colouring or stamping I use products from Genesis Creations. They have a fabulous range of Australian made and developed non toxic fabric paints and liquid colours for fabric colouring (dyeing).
I have a neat tip for colouring the lining fabric to match the outside design. When I am finished with the small foam roller that I use to apply the paint to the stamps, I soak it in a small container of water. That coloured water is then used to colour/dye the fabric. Genesis Creations fabric paints have a soft base cold cure formulation which means they are colour fast and fully washable after a few days of curing. Curing is as simple as leaving the fabric to dry and sit for a few days. So no nasty chemicals to set the dye and you are using something you would normally wash down the sink!
I'll include a more detailed post about how to do this within the next few days.