Directly to Kalymnos airport with daily flights of Olympic airlines from Athens.
There are also daily flights of Olympic airlines & Aegean airlines to Kos airport. From there you can reach Kalymnos in 20 minutes by ferries chartered by the Municipality of Kalymnos.
There are also daily flights of Olympic airlines & Aegean airlines to the airport of Rodos. From there you can come to Kalymnos by catamaran in three hours.
You can find many charter flights from a lot of European cities directly to the airport of Kos. From there you can reach Kalymnos in 20 minutes by ferries chartered by the Municipality of Kalymnos.
By boat
From Piraeus there are a lot of liners which reach Kalymnos every day.
There is a boat connection to Kalymnos from all the neighboring islands on a daily basis.
From Thessaloniki, Alexandroupoli or Kavala there is a boat reaching the Aegean islands from May until the end of September.