Yes you can!

Make sure that your devices are logged in using the same Google Play account, as it automatically saves in-game progress, also on multiple devices.

Important: You can only connect one game account per Google Play account. Should you try to save multiple user accounts on the same Google Play ID, this might result in lost progress!

To connect to Google Play:
    1. Start the Google Play Game center app on your device and log in
    2. Open the game, and enter the in-game settings
    3. Press the Google Play sign in button to connect your game to Google Play
Now you can enjoy Badland Brawl across your Android devices!