Is there any handy option for running MemSql on Google Cloud AppEngine and accessing it from dotnet application running on the same instance?
I'm not familiar with MemSql, but be aware that App Engine Flexible instances are restarted on a regular basis, and during that any locally saved data on disk will get lost, so hosting a database on Flexible is not a good choice. You may want to setup the DB on a GCE instance using persistent disk for storage.