You can use Reports > Customer Service Reports > Customer Service Activity filtering for Activity = sys:Actions Rush to report on the action button usage
What Is the function of the Rush Button?
The Rush button allows you to escalate an item in the shipping process.
eligible items are those that has not exported in a shipment batch, not charge only, AND in one of the following statuses: not yet available, item pending, Item Reg. Hold, item pay ready, item ship ready, item invalid, item decline authorization
Click on the Rush action button from the Order Detail screen
Select the items you wish to rush.
If you want to select all the items, click the Check All link.
If you want to deselect all the items, click the Uncheck All link.
Choose a reason from the reason drop down list.
Enter any notes about the item in the notes section.
Click the Save button to save your changes and mark the selected items as shipped.
To cancel any of the current changes you have made, click the Cancel button.
This will close the Mark Item as Shipped window without saving any changes.
For any items on back order, when inventory is received into the system, items checked for Rush will be assigned inventory over paid orders and/or older orders.
Once the order has exported in a shipping file, the Packing Slip will display Shipping Method = RSH