Train from Milan to Chambonix, France

Take the bus it is direct non stop

https://www.flixbus.com/bus-routes/bus-milan-chamonix-mont-blanc

Or you can read about this topic to see what others recommend
https://search.ricksteves.com/?utf8=%E2%9C%93&query=Chamonix++to+Milan&button=

It is really out of the way to get to Chamonix from Milan by train. The best way is to go from Milan to Torino, changing trains for Aosta, and then catching a bus to Courmayeur, where he can pick up the bus to Chamonix via the Mont Blanc tunnel.

Other than that, he can catch the Flix bus and head to either Geneva or Courmayeur and pick up the Mont Blanc tunnel bus from there.

If you’re traveling light, take the bus 🚌 to Courmayeur and hop the Skyway Monte Bianco, change to the Panoramic cable cars 🚡 (if they’ve been repaired and are running) and then hop on the Aiguille du Midi cable car 🚠. Voila, you're in downtown Chamonix!

You can take an EC train from Milano to Geneva, direct with no changes about 4 hours, then take a shuttle bus (AlpyBus is great with 9 passenger vans) to Chamonix. The shuttle ride is under an hour.

The quickest and easiest option is the one Laurel suggested. Take a direct train from Milano Centrale to Geneva main station (3H:58M) and then use a pre-booked Shuttle from there to Chamonix (ride is about an hour as I recall - the Shuttles pick up at the main station).