Are there nonstop flights from Moscow (SVO) to Almaty (ALA)?

Yes. Aeroflot fly this route. Flight time is about 4h 10m.

What is the fastest connection from Moscow (SVO) to Almaty (ALA)?

via Samara ≈ 4h 41m, via Orenburg ≈ 4h 41m, via Kazan ≈ 4h 42m (estimated flying time, excluding layovers).

from 37,000 JAL miles (economy, one way, based on the published award charts).

Sheremetyevo International Airport (SVO) to Almaty International Airport (ALA)・3,123 km

Nonstop flights available (1 airline). Flight time about 4h 10m. Nonstop return flights also operate.

With milesJAL 37,000 miles+ (via DOH)Economy, one way, estimate. Tap a connection for miles by cabin.

35 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.