Hey renegade, I usually use the tan RIT dye as the base for any flesh color, adding very little (if any) pinks or oranges or browns depending on the desired result. Dyeing seems like it could be an exact science, but in reality it never is. You can keep track of the amount of water and dye, the temperature of the water, the length of time and still your results will vary. All it takes is variance in the lot of fleece or differences in the foam (which there always is - since making foam is not an exact science) and your results are never exactly the same.
You just have to experiment. Test small pieces in the dye bath and add the dye gradually to get the color you're looking for. If you're planning on dying foam and fleece the same color, that will take some playing around with as well. Foam takes the dye differently than the fleece. You'll probably notice the greatest difference in the vibrance of the color. Antron fleece usually turns out more vibrant than the foam so you'll have to adjust the amounts of dye and water temperature to compensate. The less dye and cooler the water the less vibrant the color.
I think the picture you posted is one of LabRat's puppets, if I'm not mistaken. You may want to ask him what he used as a starting point.