The only sure way to save your progress in the game is to sync your game with Apple or Facebook. You can do this in Settings (the gear icon in the corner), or in your profile by clicking on your avatar. By syncing your game, your progress will be permanently linked to your Apple or Facebook account, and you won't lose it even if you reinstall the game or download it on your new device.
Note that if you want to play on multiple devices at the same time or completely transfer your progress from one device to another, your game must be connected to your Facebook account.
If you need help transferring your progress, please contact our support team and they'll be happy to help!