SPD 2013 REST API? how to extract checkbox field values from d/results?

the checkbox values are returned same as the way other fields are returned, they are Boolean.. you can try below code

  var item = ''; 
  return $.ajax({
        url: _spPageContextInfo.siteAbsoluteUrl + "/_api/web/lists/getbytitle('"+listName+"')/items?$select=IsClosed",
        type: "GET",
        data: JSON.stringify(item),
        headers: {
          "Accept": "application/json;odata=verbose"
        }
      })
      .done(function(data) {
        for(var i = 0;i<data.d.results.length;i++)
        {
            Console.log("IsClosed : "+data.d.results[i].IsClosed)
        }
      })
     .fail(function() {
        alert("error");
      });

Hope this will help you.. Thanks