This is way too much for one day unless you are just going to look at things from the outside.
I'd get a timed entry to Santa Maria Delle Grazie for the Last Supper for as early as you can manage. There was an English tour at about 930 or so, I think. That will take about 45 minutes to see BUT you need to be there a certain amount of time ahead so you'll probably wind up with 1.5 hours here. Buy your ticket from the official website as soon as they go up for sale.
The Duomo, if you do the Rooftop and see the interior takes a couple of hours. Get the Fast Pass to take the elevator to the roof but then you'll have to walk down. The fast pass comes with entry to the museum across the square but I didn't have time for that.
Afterward you can walk thru the Galleria Vittorio Emanuele to La Scala and see it from the outside (did you want to go in?).
I added in the Pinacoteca Ambrosiana which is near the Duomo but did not do anything else on your grocery list.
What is it about the sites you have listed that makes you want to see them? For myself, I wanted to see Leonardo's work before it completely flakes off, wanted to see the Raphael cartoon (drawing) of the School of Athens in the Pinocateca, and wanted to do the rooftop and interior of the Duomo. I was looking for somewhere to sit and eat dinner so walked thru the Galleria for that.