Hi @ DylJur,
Do you want the action “set up automatic replies” run at the midnight of the day when the trigger “when an upcoming event is starting soon” is fired?
Or do you want the “Start Time” field and the “End Time” field of the action “set up automatic replies” would be the midnight of the event’s start and end time?
If you want the action “set up automatic replies” run at the midnight of the day when the trigger “when an upcoming event is starting soon” is fired, you could add a “Delay until” before the “set up automatic replies” action on your flow.
You could create a flow as screenshots below:


The expression of the Delay until as below:
startOfDay(addDays(utcNow(),1))
When an upcoming event is starting soon, such as the trigger would run at “2018-03-07T11:00:00Z” the flow would run successfully as below to delay the run of “set up automatic replies” action until the midnight “2018-03-08T00:00:00Z” :

If you want the “Start Time” field and the “End Time” field of the action “set up automatic replies” would be the midnight of the event’s start and end time, you could create a flow as below:

The expression of the "Start time" as below:
startOfDay(addDays(triggerBody()?['Start'],1))
The expression of the "End time" as below:
startOfDay(addDays(triggerBody()?['End'],1))
When an upcoming event is starting soon, the flow would run successfully as below:

Regards,
Alice Zhang