Kennel Cough in dogs will stimulate a coarse, dry, hacking cough about three to seven days after the dog is initially infected. It sounds as if the dog needs to "clear it's throat" and the cough will be triggered by any extra activity or exercise. Generally, dogs that have this do not throw up phlegm because the cough is usually a dry one. In fact, their general state of health and alertness will be unaffected, they usually have no rise in temperature, and do not lose their appetite. Seems your dog is still hungry, so that's a good thing.
Many dogs that contract Kennel Cough will display only minor signs of coughing that may last seven to ten days and will not require any medication at all. The majority of dogs with the disease continue to eat, sleep, play and act normally... except for that annoying, dry, non-productive coughing that seems so persistent. Kennel cough should not cause your dog to throw up his food.
Other disorders such as Blastomycosis, Valley Fever, Heartworms and even cardiac disease might display similar sounding coughing. Keep a close eye on your Lab