Walnut plywood is readily available from suppliers to cabinet shops but you won't find it or be able to order it through most big boxes or standard lumber yards. The grain is called plain sliced, veneers were sawed from boards, not rotary cut from a log like construction plywood, and the slices are matched. 3/4" plain sliced walnut plywood will go close to $100/sheet. Veneering is quite complicated and involves far more than gluing on some veneer.
In most of the US there are architectural cabinet shops. The general public doesn't know that they are there, they don't do residential work, no kitchens, they typically do all the banks, hospitals, government buildings, schools and other institutional work you normally see around your town or in your travels. Most of these shops are hidden in an industrial area, no signage. These cabinet shops need large quantities of plywood, hardwood and other supplies. The suppliers are similar, they don't deal with the general public, you can't go to most of their yards since they are B to B only and they don't allow non employees into the work area, with some exceptions. Look in your yellow pages for Architectural woodworking or millwork shops. Call and ask where they get their plywood. You'll be surprised what exists under the radar unless you are in the boonies.
You don't have your location listed. For difalkner in LA, there is Specialty Millwork and Casework in Shreveport, probably a couple others.