In order to transfer your cloud save from one device to another, you need to first make sure you are logged into your Google Play or Apple account in-game on your first device.
Then install the game on your second device and make sure that you have access to a steady internet connection. Once the game is installed on the new device, log into your Google Play or Apple account in-game on this new device and wait for the synchronization to be complete.
Please make sure that you really wait until the synchronization is complete before you launch a run on the new device as otherwise it can overwrite your previous progress!