You paid for the app, and that's applied to your account - so whatever device your account is logged into - you have the app.
As for the sync over devices - not sure on that - though there is the function to save your data in the app to a folder or online storage such as box.com, dropbox, Google Drive etc.
Under Settings, ( gear icon ) scroll down, and find Backup rifles - once backed up, from your other device you can then go to your chosen method, ie Google Drive, and 'Yes, import rifles from Google Drive.'
Hope this helps.
I did this when had a new phone - just uploaded and down loaded from old to new ...
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