Critter Catcher, If your dog is heart worm free and its not true kennel cough, there is a chance that this cough is related to high of a protein % in your dog food. You can find out real fast by changing his diet for one week. You can feed him plain corn bread and red beans ( high carbs-low protein), I know this sounds a little strange but it comes from my old consulting DVM who practiced for 45 years. He found this condition to be more prevalent than most Vets think.
This type of dog can't metabolize all the protein and the first sign is the cough. In bad cases it will progress to Seizures. I had one dog that was to the seizure stage and I fixed her in 4 days with the beans and corn bread, I could not believe it, haha. You might give it a try, just so you know and its also a great reason to cook beans and corn bread for yourself

This disorder is the most prevalent in high strung hunting or working dogs and has to do with liver function.
Good luck,
Paul T