Unfortunately it is not currently possible to export milestones through the Excel Add-in.
This is a limitation within our Excel Plugin as the plugin only supports WSAPI 1.0. Milestones were introduced after the Plugin was written and a WSAPI 2.0 version is needed to access Milestones.
You can export the Milestones themselves from the Plan > Timeboxes page. One current workaround to export items along with their milestone would be to use the Custom List App which does support WSAPI 2.0 and will allow you to export data.
If you need to export items with their milestone you can use a Custom List app available through the App Catalog to export a story along with its milestone.
1) Go to the custom page or dashboard that you wish to add the Custom List app to.
2) Click the Gear in the upper right of the page and select the Add App option
3) Select the Custom List (formerly Custom Grid) app from the catalog and add it
4) Select User Story for the Type and save
5) Add the Milestone column, along with any other columns you would like to export
6) Click the Import/Export/Print icon in the upper right of the Custom List app and select Export to CSV
The other alternative which may be a bit more complicated, requires coding resources on your end, is to use WSAPI 2.0 and the SDK to create custom App that extracts the data required. You can find information about this process through the links below.