Is There a Report Outlining How Many Times a Promotion is Applied?

Commerce7 has a Query builder and you can create and Order Query with Coupon Used as conditions. For example, this Order Query below will compile a list of all orders the Promos are applied:
Here is a link to our documentation on How Do I Create Queries for Orders? for more information on how Order Queries work.
Once you have set the conditions, you can execute the query and a .csv file will be emailed to you. The file will have the same columns as the order export.