Here at this links, most of your questions will be answered.
Planning a trip to Kalymnos is very simple. You can wait for the charter flights directly to Kos in the period from May till end of October, or try the low-cost carriers like ryan-air or easy-jet if you travel outside this season.
There are so many options and i would be glad to help you out.
For any questions, send me an email; firstname.lastname@example.org