Are there nonstop flights from Moscow (VKO) to Baghdad (BGW)?

Yes. Iraqi Airways fly this route. Flight time is about 3h 29m.

What is the fastest connection from Moscow (VKO) to Baghdad (BGW)?

via Yerevan ≈ 4h 1m, via Tbilisi ≈ 4h 2m, via Baku ≈ 4h 23m (estimated flying time, excluding layovers).

from 30,000 ANA miles (economy, one way, based on the published award charts).

Vnukovo International Airport (VKO) to Baghdad International Airport / New Al Muthana Air Base (BGW)・2,541 km

Nonstop flights available (1 airline). Flight time about 3h 29m. Nonstop return flights also operate.

With milesANA 30,000 miles+ (via IST)Economy, one way, estimate. Tap a connection for miles by cabin.

11 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.