My doctor says his clinic wants coughing patients screened by video. how can he tell if i have coronavirus or the flu without listening to my chest?

Telemedicine: Listening to the chest is unnecessary to diagnose COVID-19 or any other infection. It can help tell whether an infection involves the lungs, i.e. pneumonia, but chest xray is much better. (Neither one is much help knowing the cause.) For care of any suspected respiratory infection (colds, flu, etc), telemedicine or other kinds of non-personal provider contact will become increasingly common.

Telemedicine: If you have more severe illness your doctor will probably have you be seen in-person. However, a lot of cases are being handled virtually or over the phone. Your doctor should be able to get a lot of information from your verbal history. The diagnosis is actually cinched through testing.