It's actually really simple - feathers are protein, so you dye them the same way you would wool or silk. Basically you need an acid dye, and heat, and a dyepot you will not use for food ever again! You can do it on a stove top no problem, and acid dyes should be pretty readily available at craft stores. If not, dharmatrading has a RIDICULOUS colour range, and their procion mx dyes can be used just by substituting white vinegar for soda ash to fix the colour! (I dye stuff a lot)
Point in case, I could use a few red and black feathers for various projects and given that uncoloured they're often cheaper...