You can visit Kos with cheap flights and then use the small feries from Mastihari to reach Kalymnos.
For more details about flights you can visit the websites below:

• Thomas Cook Airlines
• Easyjet

The flight to Kos (IATA Code: KGS) lasts 35-40 minutes from Athens airport. When arriving to Kos gο to Mastichari port, just a few kilometers from the airport,and then take the ferry to Kalymnos.
The trip with the boats “Kalymnos Star”, “Kalymnos Dolphin” and “Ilias T” to Kalymnos takes about 15-20 minutes.
The trip with the boat “Olympios Zeus” to Kalymnos takes about 45-50 minutes.
For detailed itineraries please check the links below.

• From Athens Airport to Kos with Olympic Airlines
• From Athens Airport to Kos with Aegean Airlines
• From Mastichari Port to Kalymnos with “Kalymnos Star”, “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 lasts 45 minutes with Olympic airlines (OA) or Astra Airlines. Kalymnos airport IATA Code is JKL.

Check the link below for flight schedules:

• Olympic Airlines
• Astra Airlines

From the island of Rhodes you can choose between the Ferry or a smaller and faster boat to Kalymnos.The trip takes 3 to 5 hours.
The other option is to flight to Kos or the other surrounding islands and take a boat from there.

• From Rhodes Island to Kalymnos with Ferry or Catamaran

An exciting and authentic Greek way to travel. Travel directly and cheaper.
All ships are comfortable and have enough free space for everyone.
The cabins are available for up to 4 people.

The journey takes approximately 10 – 12 hours.

Check below for schedules:

• From Piraeus Port to Kalymnos