Were the X-Rays read by a radiologist? Reading an X-Ray is very subjective, and X-Rays usually don't show lesions in the trachea, so maybe endoscopy is indicated.
Have abdominal X-Rays been performed? If there is a mass in the abdomen that is large enough to push against diaphragm it could cause a breathing obstruction. A large amount of abdominal fat could also do this and even has a medical name called: Pickwickian Syndrome.
Lastly, your dog could go on a short course of steroids since the steroids act as an anti-inflammatory it can help with the bronchial inflammation. Dogs can also get an asthma like problems, such as asthmatic bronchitis, that may no show up on an X-Ray if the X-Ray is NOT taken during an episode, though it is rare. Steroids help with asthma also.
Xrays were done and they showed nothing.
You should allow them to perform an echocardiogram, and endoscopy, if your vet deems it necessary.
He may have heart disease or the dog version of COPD (chronic obstructive pulmonary disease, aka: old dog lungs), or there could be masses in the lungs, or a tracheal disease. As a dog ages some of the connective tissue in the lungs becomes replaced by fibrotic tissue, and the lungs can no longer expand as well as they used too when the dog was younger. Or, if your dog does have heart disease it would be a good idea to find out, since heart medication can be very helpful.