I had this happen to a charcoal wool coat of mine. My fix wasn't perfect, but it helped lighten up the burn spots from black to charcoal.
Take a fabric brush and comb out the ash, if there's any left on the jacket. Then dab out the rest with some water or something, let it dry, and comb it again. Then if the coat is navy, charcoal, or lighter, take some dark women's powder makeup and use it to dust the burn spot. Apply and comb to match. Unorthodox, yes, but it mostly worked.