He probably got the kennel cough from the actual kennel cough vaccine - was it given by the rescue where you got him from...? Btw, the kennel cough vaccine is not a core vaccine, so I would not get it again.
Get these episodes he's having on your phone's video. It could be the kennel cough, but it also sounds like it's reverse sneezing.
http://www.yorkietalk.com/forums/die...d-trachea.html