Are you talking artic fox to dye ? It takes dye easily, the biggest problem is the skin is so thin most of the time that the skin can disintegrate if you let it sit in the dye bath too long. Cool water dying is better than hot.
A friend with lots of dying experience dyed some arctic fox tails for me. He had lots of difficulty getting the colors like I wanted. Also, the long guard hairs take the dye differently than the thick underfur and the end result was pretty inconsistent.
Black will be your hardest color, but remember the background color of the red fox fur will change the final color. Red will probably get you maroon/burgundy, purple might look almost black when it's wet, and the black might get to black but black dyes take the longest to color the fur so you may end up with dissolved skin with loose hair at the end.
Start the dye bath by mixing the dye in until it's dissolved, add the vinegar, then start heating maybe at medium depending on your stove. Once it hits about 100 degrees, get your fur wet by using Synthrapol or my preference Dawn Detergent. Wash the fur to make sure any grease is off but don't soak it in the wash water, that will help keep the hide together. Then put the fur in the dye bath. Swish the patch often to make sure you have dye penetration through the entire piece.