Hi @ adodd25,
If you would like to add an event in the user’s Outlook Calendar, you could create an Outlook event and add the user as attendees of the event, the user would see the event invite in their Outlook and they could choose to Accept ,Tentative or Decline.
So if you want to achieve your needs, you need to create the event in the Outlook Calendar rather than only create the event in the sharepoint Calendar.
I have made a test on my side and I would offer you a workaround to achieve your needs.
I have create a sharepoint list with a column "Atendees",The “Atendees” column is a Person or Groups type column.
I have create an event in the Outlook Calendar with subject “training event20180320”.
You could create the flow as below:
When an item is created the sharepoint list “Atendees”, the flow would send an email to the user with options “Accept” and “Reject”, whether the user approve or reject，the manager would receive an email with the user’s response.
if the user choose “Accept” in the email, the flow would update the event which’s subject is equal to “training event20180320” in the Outlook Calendar to add the user as a Atendee to the event, and this action would send the event to the user’s Outlook Calendar, and the user could Accept ,Tentative or Decline it.
The flow would run successfully as below:
Regards,
Alice Zhang
