cavuman1 In case you never sorted this out.
Go to the bottom right and you will see Download all Private Messages, click on the format of your choice (XML, CSV or Text) and a pop up will open and you can save the messages. You can then go to th etop right of the table of messages where it show Messages: NN click on the checkbox which will select all the messages and then go to the drop down at the bottom right - Selected Messages: Move to folder ... , click in the box and the list will open, delete is the second option.