The answer is quite simply, no. Cup for cup, both whole wheat flour and white flour contain around 400 calories. But there is a reason for choosing whole wheat flour over processed white flour. That is that whole wheat flour has not been stripped of the nutrients and fiber naturally found in wheat, and therefore offers a much more nutritious alternative than white flour. That is to say that white flour has been stripped of many of its natural nutrients during the processing stage. Of course, oftentimes white flour is then enriched, where some of the nutrients are added back to the flour, but not in its natural form.
On this site, you will find that many of the recipes use whole wheat flour in place of or partially in place of white flour simply because it is healthier, offering far more dietary fiber as well as more iron, calcium, protein, and other nutrients than white flour. When you are eating a low calorie diet plan, it is important that the calories you are feeding your body are loaded with as many nutrients as possible. That is why choosing whole wheat flour over white, though it won't save you any calories, is a good choice if you are trying to eat a healthy diet.