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Hi,
In addition to allowing port 3306 connections to pass through your firewall, you will also need to configure the MySQL server to listen on the public (or private) network interface so that it can accept external connections. You can do so by editing /etc/mysql/my.cnf, setting bind-address to 0.0.0.0, and restart MySQL.
Exposing your MySQL server publicly is not recommended however. Use SSL connections only, and only allow your app server to connect using ufw.