You can play your game on more than one device, but your game will need to be connected to your Facebook profile.
You can do this by following the step below:

1. Download the game on your new device.
2. The first time you open the App, you will get a pop-up requesting to connect to Facebook, accept the request and follow the instructions given by the App itself.

If by mistake you declined to do so, don’t panic as there is another way.
Just finish the tutorial and then follow the steps as explained below:
1. Click on the Options button (Upper right corner) and click on Login.
2. Click on "Log in" button.
3. Select "Claim". (Note that if you already have played Dragon City, this will not give you the items stated as you have to be a new user).
3. Your Facebook account will appear as default as the first option, select your account and click on “Continue with FB PROGRESS”.
4. Please be careful NOT to choose the wrong account, for example, the second option is the game account which is just level 2, and as the App tells you, it is NOT RECOMMENDED!!!.
5. If you mistakenly choose the low level account, the App will warn you, please click “NO” to exit and then select the Facebook account.

Please keep in mind that once an account has been reset, the progress is lost and cannot be brought back.