Browser applications auth used to be managed using the Implicit grant of the Authorization Server. I successfully implemented this using Spring Security Oauth.
This approach has several drawbacks:
Currently the recommended option is using Authorization code flow with PKCE for browser applications.
How could this be implemented in a Spring Boot Authorization Server with spring boot oauth?
No, it does not yet support PKCE, though there is a ticket for it.
Note also that Spring Security's OAuth support is in a bit of a transition phase right now while it is migrated into Spring Security proper. Feel free to follow this feature matrix to see where progress is at.
UPDATE: Spring Authorization Server now supports this feature.