is it an actual cough or more like they sound like they have something stuck in their throat? sometimes it can be what's called 'pharyngeal gag reflex' or reverse sneezing.
Here's my video of Momo, @ 13 secs in he does the reverse sneezing which he does once or twice a day, u'll need your speakers turned on to hear it:
If your vet suspected it was kennel cough, he would have prescribed anitibiotics...they can tell if the pup is congested w/the stethoscope.