Kalymnos has its own airport where you can fly from Athens with Aegean airlines or Olympic airlines (1 hour, 2 flights a day).
Most people choose to fly to KOS, a 20-minute ferry away from Kalymnos. KOS offers a wide range of low cost and airlines depending your country.
By Boat from Athens:
If your flight is to Athens, you can go to Piraeus (the main port) and from there you you can take the ship to Kalymnos (11-13 hours, 3 days a week). For more information visit the web site of Bluestar Ferries ( 11-13 hours, 3 days a week)
Small Planet (Paris- Kos)
From Kos, you will need to take a taxi (15 euros) or the bus to Mastichari port. Many people will go to Mastihari as many hotels are there, so it is very easy to share the taxi when you arrive at Kos airport.
Ferries schedule from KOS (Matihari Port) to Kalymnos (Pothia Port) (schedules vary depending month)
With Kalymnos Star (30 minutes)
Kos – Mastihari to Kalymnos – Pothia
Daily :8:00; 11:00; 13:30; 16:30; 22:30 (the last boat will wait for the last arrival from Athen.
Pothia – Kalymnos to Mastihari - Kos
Daily: 5:30; 9:30; 12:30; 15:00; 18:30
With ANEM Ferries (45 minutes)
From Kos To Kalymnos: 9:00; 14:45*; 18:00
*except Tuesday, Wednesday and Sunday
From Kalymnos to Kos: 7:00; 13:30*; 17:00
* except Tuesday, Wednesday and Sunday