Are there nonstop flights from Tallinn (TLL) to Amsterdam (AMS)?

Yes. AirBaltic fly this route. Flight time is about 2h 14m.

What is the fastest connection from Tallinn (TLL) to Amsterdam (AMS)?

via Copenhagen ≈ 2h 44m, via Hamburg ≈ 2h 45m, via Stockholm ≈ 2h 49m (estimated flying time, excluding layovers).

from 15,000 JAL miles, from 15,000 ANA miles (economy, one way, based on the published award charts).

Lennart Meri Tallinn Airport (TLL) to Amsterdam Airport Schiphol (AMS)・1,472 km

Nonstop flights available (1 airline). Flight time about 2h 14m. Nonstop return flights also operate.

With milesJAL 15,000 miles+ (via HEL)ANA 15,000 miles+ (via FRA)Economy, one way, estimate. Tap a connection for miles by cabin.

34 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.