Are there nonstop flights from Las Vegas (LAS) to Rapid City (RAP)?

Yes. Allegiant Air fly this route. Flight time is about 2h 6m.

What is the fastest connection from Las Vegas (LAS) to Rapid City (RAP)?

via Denver ≈ 2h 45m, via Phoenix ≈ 3h 9m, via Mesa ≈ 3h 10m (estimated flying time, excluding layovers).

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

Harry Reid International Airport (LAS) to Rapid City Regional Airport (RAP)・1,355 km

Nonstop flights available (1 airline). Flight time about 2h 6m. Nonstop return flights also operate.

With milesANA 15,000 miles+ (via DEN)Economy, one way, estimate. Tap a connection for miles by cabin.

5 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.