Are there nonstop flights from Phuket (HKT) to Kolkata (CCU)?

Yes. IndiGo fly this route. Flight time is about 2h 46m.

What is the fastest connection from Phuket (HKT) to Kolkata (CCU)?

via Yangon ≈ 3h 23m, via Bangkok ≈ 3h 43m, via Bangkok ≈ 3h 44m (estimated flying time, excluding layovers).

from 15,000 ANA miles, from 23,000 JAL miles (economy, one way, based on the published award charts).

Phuket International Airport (HKT) to Netaji Subhash Chandra Bose International Airport (CCU)・1,930 km

Nonstop flights available (1 airline). Flight time about 2h 46m. Nonstop return flights also operate.

With milesANA 15,000 miles+ (via BKK)JAL 23,000 miles+ (via KUL)Economy, one way, estimate. Tap a connection for miles by cabin.

13 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.