If you're mic'ing your equipment, this probably won't apply, but it will be of interest to drummers that play unplugged. , it is of interest. Laying the washboard on the snare drum with snares off drum amplifies it quite well. Using a different drum produces a different tone.
Music for snare drum can be read directly for the washboard. What would be press rolls can be played as drags on the washboard, and the rest exactly as if they were on the snare drum - apart from the absence of bounce, of course. If you get a hardwood-framed washboard, the sides and ends can be used to play woodblock effects.