Is there a way to get a listing of member's shipping addresses?

Tutorial

On the right side of the Control Panel (click on the on the top right to open), under 'File Import/Export' choose 'Export Mailing List' or 'Mailing Labels by Date.'

Exporting a mailing can be found under File Import/Export Export Mailing List

Creating Mailing Labels can be found under File Import/Export Mailing Labels by Date

This will allow you to have a list of shipping addresses for specified parameters which can be used for a mail merge or shipping labels.