Make sure you have "Google Play Games" installed. It is required for account linking and it is not installed on Android device by default. Search for "Google Play Games" in the Play Store and install or update it. Once it is installed, run it and make sure that it is signing into your Google account. After this, launch Battle Legion and your old account(s) should appear. If not, try linking a new account and the game will ask if you want to link the new account or retrieve an already linked one.
If you still have problems accessing your account, don't hesitate to get in touch with support using the speech bubble in the top right corner of this screen.