How to get the public IP address for an ALB that is in front of ECS services?

You technically dont, because the alb should be sitting in two different az’s. You route it based off the dns name you get from the output of the resource.

For my case I would like to add the public IP address to the list of whitelisted IP address for DB access so that my services can send requests. Which IP address would be the one I would be providing?

You would want to create an scheduled job that does a dns lookup on the alb FQDN then update your firewall as needed. The private IP's are assigned via DHCP so you may have a few outages.