If drying racks are close enough to a fire, for the sake of argument let's say radius 5-7, anything drying should get a slight buff to its drying speed. If the fire goes out, whatever's on there continues drying at the base rate. I'm not sure what a good rate buff would be--maybe max 15% faster than base?
Would be useful to keep fires burning at least semi-continuously near drying racks, and be another resource suck to balance it a bit.