App engine css not updating
Delete any existing rules, since they may conflict with the one you will create now.
Create a new rule by clicking on the 'Add rule' button.
When this (if this is what happens) happens, I can confirm that no amount of cache-busting browser work will help.
The Google CDN servers are holding the wrong version.
The cache in Google Cloud cannot be manually flushed, so instead I would recommend you to change the expiration time to a shorter period (by default it is 10 minutes) if you want to test how it works, and later setting an appropriate expiration time according to your requirements.
Bear in mind that you can change the static cache expiration time both for all static files or for just the ones you choose, just by setting the proper element in the Browser.
Other people has had the same problem (CSS File Not Updating on Deploy (Google App Engine)), and it looks like is related to Google CDN cache but, as far as I know, there isn't any way to flush it.
When performing changes in static files in an App Engine application, changes will not be available immediately, due to cache, as you already imagined.