I can't say if this website is accurate, I would always ask my vet, but it does say:
Puppy Kennel Cough
There are several home approaches for puppy canine kennel cough treatment that can be tried for a puppy (or adult for that matter).
1) One home treatment for a puppy with kennel cough is to try
Pediatric Robitussin 4x per day. This approach has been used for dogs as young as two. If your puppy does not respond, antibiotics are called for.
Check the label to make sure the medicine does not contain ibuprofen or acetaminophen since these can cause liver damage. Ask your veterinarian for the correct dose (no more than 1/2 teaspoon to avoid overdose).
Canine Kennel Cough Treatment
Note it's saying for dogs as young as two, why would they call that a puppy?