Painting skirting should be an easy task, however, you need to avoid getting paint on the floor (or carpet) as well as avoiding dust and fluff being picked up by the brush and transferred onto the paint.
Buy a 100cm piece of thin, stiff cardboard from any stationers and slide this under the skirting. This will not only speed up the process (you will have to take less care cutting in at the bottom), it will also protect the floor and stop dust and dirt sticking to the brush.