Baggage check at Milan train station .....itinerary for last supper viewing.

When will you be in Milan? Not soon I hope. If you want tickets to see the Last Supper you must get them the day they become available (2 or 3? months in advance). They go quickly, within minutes. Large tour groups buy them all up. There are very few individual tickets left. We go ours by calling from the US one minute after they went on sale for the day we were going to be in Milan.

Or, you can take a walking tour of Milan which includes admission to the Last Supper at a very large markup.

First you have to secure your entry time to get into the Last Supper. Once you have that, you will know what train to get to Florence. Often the only time you can get will be at the end of the day. Trains from Lake Como run all day, as do trains to Florence. The last Freccia to Florence is at 20:50 on a week day.
PS. I don't see any 15:10 trains to Florence, only an IC train to Bologna, then regional connections to Florence. Why do that when there are so many fast direct trains?

I checked luggage at the Milan train station a little over week ago. The luggage check station can be a little hard to find, but once you do--you might want to go in the express lane which checks your bag for 12 Euros, no specific duration. The non-express line is six Euros plus a Euro per half hour (or something like that). There were tons of people standing in the non-express line, zero in the express line. For me checking a bag for six hours it was going to be about the same either way. Your mileage may vary, as you may have many bags to check. But if you go for the non-express line, in mid-May around 10-11 a.m. I can tell you that line was about 20-30 minutes just to check a bag. I found this whole thing to be a monumental hassle. (My hotel's luggage storage filled up early on my day of departure, noted in my booking.com review). As an added bonus, the restrooms at the Milan train station are way the other end from the luggage storage. Sorry to sound so cynical, my point is don't expect checking a bag at Milan train station to be that efficient. Expect it to take longer than you expect it to take.

"As an added bonus, the restrooms at the Milan train station are way the other end from the luggage storage."

Yes, but the McDonald's is close by. We used their restrooms for free. The station restrooms charge a fee.

Also, if you plan on getting to the Last Supper by metro be conservative in estimating transition time to get there. Getting a ticket, finding the entrance, navigating your way to the train you need, oops wrong turn (backtrack), next train in eight minutes, etc. When you get there, will you need to check the backpack / is there a place to check the backpack? If no, does the backpack have anything in it that would prevent you from passing security? Is there a restroom near the Last Supper church, someone needs to use the restroom. My point is there are a lot of opportunities for circumstances to slow you down, so make sure and build in some time for logistical mistakes. Trying to zip in and zip back out in a big city that you are not especially familiar with can be really challenging. Milan can be especially difficult before you know the ropes, so plan for that.

While in Milan 2 weeks' ago, I scored a single for the 1830 group less than a week before I left for my trip. Also, there was a couple from Australia who scored 2 tickets for the same time not 2 weeks' before they arrived. I " scored" on tiqets.com. Paid €28 and was very surprised and happy. Once I started looking, I was inundated with offers at all kinds or prices, so good luck-you never know.