If you wish to add a Doctor just visit a patient's page, click "Edit patient", and then manually type a new vet name into "Doctor on Duty" field. Please see the screenshot:

To send a Doctor from ezyVet into Smart Flow all you need to do is to go to 'Users'/'Resources' section in ezyVet under the Admin section, select the 'Sync with Smart Flow' button and make sure you have chosen 'Yes':