Thanks - in the case of Flow #2, could you please switch from the HTTP action to the built-in Microsoft Teams action? It looks like you are getting back a 302 redirect which Flow is not following (however, we can avoid the issue entirely by using the Microsoft Teams connector which handles all these cases automatically).
If this still does not work / you are facing issues - could you please send me the additional details at chlama@microsoft.com? I can loop in more folks to help debug it more deeply.
The Microsoft Teams connector is now available - the connector and its associated templates are visible here: https://flow.microsoft.com/en-us/services/shared_teams/microsoft-teams/