Until secrets were introduced, a common way to pass information to containers was through environment variables. While that will continue being the preferable way for non-confidential information, part of the setup should involve secrets as well. Both should be combined. The question is which method to choose and when.
The obvious use case for Docker secrets are secrets. That was obvious, wasn't it. If there is a piece of information that should remain invisible to anyone but specific containers, it should be provided through Docker secrets. A commonly used pattern is to allow the same information to be specified as either environment variable and a secret. In case that both a set, secrets should take precedence. You already saw this pattern through Docker Flow Proxy. Every piece of information that can be specified through environment variables can be specified as a secret as well.
In some cases, you might not be able to modify code of your service and adapt it...