Jogging will burn calories, so you will lose fat, assuming you eat sensibly as well. The fat will come off everywhere, so in time your stomach and chest will carry less fat.
Jogging will not particularly develop your stomach muscles but will do wonders for your legs and bottom.
Jogging is an aerobic exercise benefitting the heart, lungs and circulation. By itself its not a weight reducing exercise and the flab will stay on the stomach and chest as the muscles are not distended. The legs will get firmer and the bone mass may improve without you needing an osteopath in later life.
One of the nicest ways to flatten your tummy is to go swimming regularly..You don't need to go like the clappers either, just a load of nice gentle Breast Stroke lengths every week..Works wonders...Im talking from experience...
A really good way to flatten your tummy is to do sit-ups, lay flat on the floor with your knees bent (you can tuck your toes under the bottom of the armchair) and sit up touching your knees with your forehead, start with just 5 then work your way up to 15 over the course of a week, you'll notice results very quickly, you'll be surprised!