Hi Mike, for security reasons, you will need to activate Duo Mobile for each of your devices individually as it relies on a secure, unique key for each authentication device.
While you can’t sync accounts, there is a new feature, Duo Restore, that will allow you to securely backup and restore Duo-protected (not third-party) accounts in Duo Mobile. This feature will allow you to go through the re-activation process directly from any additional iOS devices. You can read about it here: help.duo.com/s/article/duo-restore