
The vaccine that's in the puppy jab is to protect against "parainfluenza" which is just one strain of cough. A lot of vaccines that are intra-nasal will protect against "bordatella bronchiseptica" -which is a more common strain of cough.
Pups can be vaccinated from 2 weeks of age with one of the intranasal ones.- trouble is - there are just so many different types of cough - it's impossible to immunise against them all.
So even if your dog is vaccinated - they can still get kennel cough!