I have never use it for this and to honest I do not much like Rit Dyes. I use Procion or a fiber reactive dye. Dyeing is not very complex and I do mine in zip lock bags on the kitchen table. I get my supplies from Dharma Trading but procion dyes are readily available from most art supply stores. I use plain salt and sodium carbonate as a dye fixer. Sodium carbonate is also called washing soda but you can get it very cheap at pool supply stores. You will also need Synthropol which is a soap to so the final wash in. I use my washer, with no staining problems. If you want to get a dye book I highly recommend "Hand Dyed Fabric Made Easy" by Adriene Buffington. I get some really fabbo fabs with the zip lock method. It is hard to get it wrong.
I suggest you go to Dharma's web site and look around you might like what you see. They have wonderful blanks to dye and that is where I get my sweat and Tee Shirts for dyeing. I also recommend their bamboo socks, even if you don't dye them. They are softest, warmest socks I have ever had and every year my kids make a special request for them. I pop a couple of pair in the zip lock bag so they have matching socks. If you want to you could also try making mud with very dilute craft paint half paint and half water. Mix red and green for a brownish mud, wet the cloth, scrunch it up and stick it in a smallish container. You really want it scrunched in. Might be a good use for old butter tubs or cheapo plastic containers, even an old jam jar would work. You will have to leave it at least overnight but it can be rinsed out in the sink and heat set with your iron. I mean really what do you have to lose? Just some time and a little muslin.