Merlot or Malbec
I've had several Pinot Noir reductions with "flatiron steaks" lately, that have been excellent. I served an older Cal-Cab, and Amarone and a Santa Rita Hills PN (closer to a Syrah, than a traditional PN) and all were quite good. In very general terms, I usually lean toward an Old World Syrah, or a PN, when mushrooms have much of a role, though several other varietals seem to pair well too. Of the two (without specific examples), I'd tend to think of a Mendoza Region Malbec to pair with the flank steak with a reduction/sauce.