You have a couple of options for customizing the login experience when you are using FusionAuth.
You can use the password grant and create your own login page. Here's an example of the password grant. But this doesn't let you use the Authorization Code grant. You can use themes to customize the login pages. You could implement the authorization code grant without ever using the FA front end. You'd have to create your own login and logout pages on the server, and then have the server communicate via the API. Not sure why you'd want to do that, but maybe it meets your needs. You could use a third party tool like Hydra and use FA for your user data store.