There is no fast way to paint fur like this. However, I do have a brush which I think is the perfect choice. I don't want to paint every hair. Not only would it drive me crazy, but it doesn't look like fur. Fur is small clumps of individual hairs.
My go-to brush is a small flat angle sable brush. It forms a tight chiseled surface when loaded with paint. For each clump I start with the point and drag the brush across the board in the direction of the fur. Here, the lighter fur will overlap the spots. Of course there will be areas where I want single hairs to overlap but the majority of the fur is painted with this one brush.
Click on the image to see more detail.