I would have a test done to determine the ph of that soil before mixing it with your garden soil. Millings from walnut trees will stunt the growth of most garden plants. Also, if the mix has oak material in it, it will acidify the soil and cause problems as well. Test it to be sure as you can’t easily remove it from the garden after the fact.
You may need to add lime and fertilizer to it while it composts. Clippings from non weed treated grass will speed the process and help enrich the soil more quickly.