Memcache backs the OOTB session store for App Engine Standard Environment, yet App Engine Memcache does not work with Flexible Environment.
Documentation for configuring Flex Env says nothing about sessions.
Of course I could implement this myself, but sessions stores are basic to most fully functional application servers, including GAE Standard Environment. Can I get a session-store with some configuration and no coding?
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For session-store you could use Cloud Memorystore, which is a fully managed Redis service for GCP. Check how to set up and connect App Engine Flex with Memorystore.
As per documentation, Memcache service is currently not available for App Engine flexible environment, but you can apply for an early access alpha here.
In the same documentation are provided also two third party memcache services which you can configure and use with App Engine flexible environment:
Out of the box session-store for App Engine Flex is currently not featured, as opposed to App Engine Standard which has this option when using Java, while Flex has the same behavior for all runtimes, with no expected differences between them.
Should you consider OOTB session-store for App Engine Flex a feature that should be added to its functionalities, please file a feature request by going through this link.
As @komarkovich pointed out, you can use Cloud Memorystore to manage sessions and perform session-store operations, however the OOTB functionality that you request is not present there either. Using DB backends such as Redis or Datastore can also manage
For a more integrated approach, you can use Firebase user session management to manage your sessions. I am not a Firebase expert myself, so I would not be able to help you further on that side, but there are good people on this community (such as Frank van Puffelen) that can help you should you have any doubts about using it.