There seems to be a limitation with the Microsoft Flow. We have tried several times to set the CDS component to run as the current logged in user. We have tried all 3 options of : Run as process, triggering user and etc. We have also created a connection under our account or a service account and these options failed. So, any record created will show under the user account that created the connection, etc. instead of the actual logged in user.
Microsoft stated that this limitation exists, so hopefully a fixed is applied soon.