The cloud syncs with DJI servers, so if you do that first you can sync back for the screens in the DJI app, but don't know if it restore the full files, such as the records that can be uploaded to HealthyDrones.
You need to copy them off using iTunes. Go to the App section of your phone/tablet (make sure the screen is unlocked), scroll the right side down to File Sharing, click on the DJI GO app icon, click on FlightRecords or videoCache, then click on the Save To button.
There are a lot of YouTube videos showing this