It depends! I like to grow quality black walnut trees, on quality sites, to a minimum diameter of 22-24 inches. Ideally, I would like to grow the best veneer quality walnut trees to 26-30" DBH.
However, it is perfectly acceptable to harvest smaller diameter walnut trees (18-20" DBH) that exhibit a lot of defect, top/crown damage, stress, decay, and slow growth rate; or walnut trees growing on poor or low-quality sites.
Do yourself a favor and contact a local professional forester for on-site technical assistance:
Directory of Professional Consulting Foresters: http://web.extension.illinois.edu/forestry/pdf/tfb-nres-202-14.pdf