I have made a test on my side, please consider take a try with the following flow's configuration:
Within your app, set the OnSuccess property of the Edit form to following:
Set(ReturnedMsg, 'YourFlowName'.Run("","").ReturnedMsg); /* <-- Getting the returned output from above flow */
Nofify(ReturnedMsg, NotificationType.Success) /* <-- Display a successfull Prompt info */ Back()