The train will get you to Milan Centrale station (and eventually to Malpensa) faster than the flight no matter what.
From Roma Termini to Milan Centrale it's a 2h45m train journey on a FrecciaRossa.
You need 45 min just to get to the airport from the city center of Rome, add 90 min for check in+security, then 1h15min for the flight to Linate, and that's 3 hours before you can even deplane. After that you have to make it to Malpensa (there is actually also a bus that connects Linate to Malpensa) and that is 90 min without major traffic interruption.
Flying to Malpensa directly from Rome is not a viable option since Alitalia discontinued that route. EasyJet is the only airline that serves that route, but the only one flight from Rome arrives too late for you.
One more note. As a matter of principle I like to stay closer to the city I depart from, if possible. I realize that your flight is in the afternoon, however I'd probably work my way to Milan the day before, and take advantage to spend a few hours in Milan the afternoon of the day before the flight. There are some nice things to see in Milan.
Then in the morning you have plenty of time for a nice breakfast. Remember that you need to be at the airport no later than 2 hours before the flight home, and that Malpensa is about 45-60 minutes away from the center of Milan (depending on the mode of transport). You should take the Malpensa Express train from the Cadorna station sometime after 11am.