If you are using the mobile app, you can do the following. If you are on the full web browser version (PC/MAC), you can go to step #3:
1. While viewing a post in a thread (such as this one) click on the 3 dots in the upper right corner
2. A screen will appear. Click on Web View
3. In web view, look for a Login button in the upper right area of the web page. Click on it
4. Login with with you AA credentials
5. After logging in successfully, you will see a menu item entitled User CP. Click on it
6. On the left column there will be a section called Private Messages. Click on the first item listed (List Messages)
7. Your messages will be listed on the screen. On the right side is a check box. Select the messages you wish to delete (using the checkbox)
8. At the bottom of the screen is a drop down menu entitled Selected Messages. From the list of options, select Delete
9. Click the Done button and click the Go button to complete the selected action