Hello Neil,
Based on this document, Binary Authorization is a service on Google Cloud Platform (GCP) that provides software supply-chain security for applications that run in the Cloud. Binary Authorization works with images that you deploy to Google Kubernetes Engine from Container Registry or another container image registry.
At this moment Binary Authorization, does not integrate with Google App Engine. However I have made a feature request to App Engine engineering team so that Binary Authorization can be integrated with Google App Engine. Please follow this link to track progress of the future request. I have also cc’ed you in the public issue so that you get notification of future updates.