Alitalia MilleMiglia - 45 mins domestic connection at FCO: feasible?

arriving from VCE at 12.15 (AZ1472) and leaving for LIN at 13.00 (AZ2038). What are the odds of making it?

45 minutes is the minimum connecting time from one flight to another, considering you're tranferring in the domestic area it won't be a problem and expecially because flights to lin depart every 10 minutes.

Out of curiosity... are you on a mileage run or something like that?
Otherwise from VCE to MIL, Eurostar train is a much much better option: it takes just 2:35

No problem with that connection. It's all within the single domestic pier of FCO, so distances are short. Even with a delay you're fine - there are very frequent flights to LIN so you'll just get rebooked to a later one.

Out of curiosity... are you on a mileage run or something like that?
Yep. Ultimate destination is LHR but I am routing VCE-FCO-LIN-LHR rather than VCE-FCO-LHR to maximise earnings.

The AZ booking engine is very MR friendly; on many occasions, it offers multiple stops for the same price as the shortest/easiest possible way.