Are there nonstop flights from Seoul (ICN) to Shannon (SNN)?

No. The fastest connection is via London, about 12h 7m of total flying time.

What is the fastest connection from Seoul (ICN) to Shannon (SNN)?

via London ≈ 12h 7m, via Frankfurt am Main ≈ 12h 31m, via Wrocław ≈ 12h 31m (estimated flying time, excluding layovers).

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

Incheon International Airport (ICN) to Shannon Airport (SNN)・9,102 km

No nonstop flights. The fastest connection is via London (LHR), about 12h 7m of flying time (layover not included).

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

None.

10 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.