You can handle the migration like any other web application. The easiest method is to transfer everything via SSH, but basics are this:
- Create a new database on the new server hosting.
- Import all Flarum tables to that database (ie, export your current database as a single file and then import it to your new database ).
- Copy all files to the new server.
- Update the config.php file with the new database name, user, password
- Point the DNS for your domain to the new server