You can recursively add the properties to a new object, and then convert to JSON:

var res = {};

(function recurse(obj, current) {

  for(var key in obj) {

    var value = obj[key];

    var newKey = (current ? current + . + key : key);  // joined key with dot

    if(value && typeof value === object) {

      recurse(value, newKey);  // it's a nested object, so do it again

    } else {

      res[newKey] = value;  // it's not an object, so set the property

    }

  }

})(obj);

var result = JSON.stringify(res);  // convert result to JSON