You can fly directly to Kos and then take a taxi to Mastichari port.  From there you can take one of the various boats to Kalymnos 

The duration of the flight from Athens to Kos is 35-40 minutes . When arriving in Kos  , you can take a taxi from the airport to Mastichari port , which is a 5-10 drive from there you can take one of the various ferries to Kalymnos.

• From Athens Airport to Kos with Sky Express
• From Athens Airport to Kos with Aegean Airlines
• From Mastichari Port to Kalymnos with  “Kalymnos Dolphin” and “Ilias T”
• From Mastichari Port to Kalymnos with “Olympios Zeus”

The fastest way to get to Kalymnos is by plane where the flight takes 15 minutes with Sky Express. Kalymnos airport IATA Code is JKL.

Check the link below for flight schedules:

• • Sky Express

From the Island of Rhodes  you can choose between the Boat and the Catamaran to Kalymnos . The trip takes  3 to 5 hours .

The other  option is to fly to Kos or the other surrounding islands and take a ferry form there .

• Rhodes Island to Kalymnos with Boat or Catamaran

The journey takes approximately 10 – 12 hours.

Check below for schedules:

• From Piraeus Port to Kalymnos