Logs are Not Nested Under Requests in Flexible VM
As you might imagine, App Engine Flexible uses a good bit of different machinery from traditional App Engine, and these different environments do log differently. It is unfortunately not currently possible to induce Flexible to log in the same data format as Classic.
If this is sufficiently important to you, you can always directly log via the Cloud Logging API, which is what the App Engine logging API ends up passing through to today. You can infer the data format to log by looking at traditional App Engine entries, though we have open a feature request to publicly document this more explicitly.
Also, as a passing note, on the Stackdriver Logging (formerly Cloud Logging) front, we're definitely thinking about ways to support this kind of denormalization of log data more generally, rather than just special-casing for App Engine logging in a specific format, as this would be broadly useful functionality. However, we don't have any specific plans or timelines that we can share at this point—just noting that this is on our radar.
You can now write nested application logs that behave similarly to App Engine Standard by following the instructions here: https://cloud.google.com/logging/docs/view/service/appengine-logs#linking_application_logs_and_requests