Beach Buggy Racing 2 supports Account Management and recovery. To begin, click on the "Profile/Settings" button on the upper left hand corner of the screen. Then, tap the "Manage Account" button.
To set up an account for the first time, you will need to enter an email address and a password. Once you've done that, you can switch over to any new device and Sign In with the same email address and password.
You can keep a single Account synced across multiple devices (like an iPhone and a Kindle Fire) by signing in on each of those devices. However, before you switch over to DeviceB, you should quit the game on DeviceA or you may experience problems.