Veterinary questions? Ask a Vet for Answers ASAP
Hi, Welcome to Just Answer. I'm Chris, a small animal Vet based in the UK. I am reviewing your question and will get back to you as soon as possible
Sorry to hear about this problem with your dog. The kennel cough vaccine is a live vaccine and can elicit mild symptoms, it takes 2-3 weeks for full immunity to develop so it is possible to see the signs you are describing during this time. If the signs are mild and he is otherwise well in himself then I would just monitor things. If the coughing/sneezing has not cleared up in a week or he seems off colour then it would be advised to get him checked by your vet.
I.hope this answers your question, please feel free to message again if you need any further help or advice.