What class?

If economy, there have been tons of fare sales to Italy this year. In fact, I believe there's one right now. For your dates, there are prices as low as the 500s. No way an award ticket beats that. For example, you can do JFK-MAD-FCO on 10/6, returning MXP-JFK on 10/15, for $587. If you have Sapphire Reserve, you can use ~39k points to book that directly on Chase's portal. If you have Sapphire Preferred or Ink Preferred/Plus/Bold, it'd cost you ~47k. Considering an economy award ticket is at best 50k (with Flying Blue) + taxes/fees/surcharges, using points in the Chase portal easily wins (it earns miles too).