Are there nonstop flights from Kolkata (CCU) to Kochi (COK)?

Yes. IndiGo fly this route. Flight time is about 2h 43m.

What is the fastest connection from Kolkata (CCU) to Kochi (COK)?

via Bhubaneswar ≈ 3h 14m, via Chennai ≈ 3h 15m, via Bengaluru ≈ 3h 15m (estimated flying time, excluding layovers).

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

Netaji Subhash Chandra Bose International Airport (CCU) to Cochin International Airport (COK)・1,891 km

Nonstop flights available (1 airline). Flight time about 2h 43m. Nonstop return flights also operate.

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

12 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.