I cannot find a video of a dog coughing, but here is a copy-paste from WebMD:
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"If your dog is hacking away or constantly making noises that make it sound like he's choking on something, he may have a case of kennel cough, or canine infectious tracheobronchitis. Although kennel cough can sound terrible, most of the time it is not a serious condition, and most dogs will recover without treatment.
(...)
The classic symptom of kennel cough is a persistent, forceful cough. It often sounds like a goose honk. This is distinct from a cough-like sound made by some dogs, especially little ones, which is called a reverse sneeze. Reverse sneezes can be normal in certain dogs and breeds, and usually only indicates the presence of post-nasal drip or a slight irritation of the throat.
Some dogs with kennel cough may show other symptoms of illness, including sneezing, a runny nose, or eye discharge.
If your dog has kennel cough, he probably will not lose his appetite or have a decreased energy level."
None of these different descriptions of coughs (variously "hacking", "choking sound", "honking", "reverse sneeze") sound like what your dog is doing though.
Bump for people in the know!