You can download patient demographics, including email address, from the patient tab:
Filter by patient population you would like a report of i.e. if you only want to email active patients, click 'All Patients' and select 'Active Patients'
Click the cloud with the down arrow to export to CSV
From the next screen you can select which fields to export by checking the box next to the field. Ensure 'Email' is selected. Then click 'Export'