You can come to Kalymnos either by ferryboat (from Piraeus or from Dodecanese islands on a daily basis) or by airplane (from Eleftherios Venizelos international airport directly to Kalymnos or via Kos).
Also, you can go from Turkey (e.g. Bodrum airport) either directly or via Kos (the most months of the year, there are frequent routes from Turkey to Kos).
You can fly to Kalymnos from Eleftherios Venizelos international airport, on a daily basis.
Find out more about the Departures and Arrivals of Kos Airport here