If you have purchased Unlimited scans, and you want to use the app on an additional device, you can download the app on the additional device using the same App Store account. Once you install the app on the second device, go to the upgrade page, and tap 'Restore purchases'. You will then have Unlimited scans on the second device as well!
Regarding seeing the same cards on multiple devices - please note the app is designed to store data locally, and that data cannot be accessed on multiple devices at the same time.
Looking to transfer your data to a new phone? See here how to do that.