I'm going to guess that you're talking about cotton and silk yarn and not unspun fiber.
I wouldn't advise dyeing silk or cotton with koolaid. Koolaid, and any acid dye for that matter won't dye cotton, it will only stain it and most if not all of the color will wash right out. Cotton needs to be dyed with either fiber reactive dye or direct dye. I definitely reccomend using fiber reactive since it's easier in my opinion ( no heating, just soak the yarn in a soda ash solution overnight, squirt it with dye, cover let sit, and rinse off,) and because it's washfast after the excess dye is washed off while direct dyed cotton will bleed in the wash forever. Fiber reactive dye can also be used to dye silk the exact same way.
I don't recommend using koolaid on silk because it just doesn't stay. It takes but washes right out. I don't know why but I know it does.
Omega acid dyes are the all in one type with the acid needed for the dye to take is already in the powder, so all you have to do is add it to water, add yarn and heat.
What you want to do is hand paint your yarns.
Here's a knitty article on hand painting: http://www.knitty.com/issuespring07/FEATdyeyourown.html
Here's hand painting instructions for a similar dye:
Basically what you need to do is wind the yarn into a skein, if it isn't in one already, soak the yarn in water with a tiny drop of dish soap or shampoo added for about a half an hour, squeeze out most of the water, lay the yarn down on plastic wrap, mix up solutions of water and dye, add the solutions to the yarn using whatever floats your boat: spongebrushes, syringes, squeeze bottles, turkey basters, eye droppers... then fold the sides of the saran wrap in and roll it up, and heat it somehow. If you want to microwave it, the usual way seems to be to nuke it for 2 minutes let it cool, and repeat about 2 more times, checking to see if the surrounding water is clear. You can also steam it for half an hour. Just be aware that whatever containers and utensils you're using should be dedicated to dyeing.
The colors might run into each other a bit, but if the fiber isn't too wet, and the dye solution isn't too weak, they shouldn't mix too much.