Are there nonstop flights from Hanoi (HAN) to Phuket (HKT)?

Yes. VietJet Air fly this route. Flight time is about 2h 27m.

What is the fastest connection from Hanoi (HAN) to Phuket (HKT)?

via Bangkok ≈ 2h 58m, via Bangkok ≈ 2h 58m, via Siem Reap ≈ 3h 4m (estimated flying time, excluding layovers).

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

Noi Bai International Airport (HAN) to Phuket International Airport (HKT)・1,664 km

Nonstop flights available (1 airline). Flight time about 2h 27m. Nonstop return flights also operate.

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

15 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.