I'm using Firebase Hosting and I several webs on my app. The two firsts webs point to the same flutter app, but the third, which is a custom domain should be a different flutter web app, but when I do firebase deploy (after flutter build web) it publishes the same content for all of them. I tried to change the firebase.json of my new flutter web app to point to mydomain.com but I get this error: "manifest.json:1 Failed to load resource: the server responded with a status of 404 "
Please, could someone guide me on how to have two different flutter web apps on the same firebase project?
Thanks!

Your question is not unique to Flutter. The configuration will be the same for all web deployments, regardless of what you actually deploy.
What you will have to do is add another site to your project. (Either that, or create an entirely new project. You have to decide which is best for your use case, but if your two apps don't share project data, then they probably shouldn't be the same project.)
Follow the instructions in the documentation. Go to the Firebase Hosting console, scroll to the bottom, and click this button to start: