Atlas will not start Mykonos flights until july.

Best option is Either to Fly Athens and connect Mykonos or from Kusadasi to Samos and Samos to mykonos by ferry.

If you have time and flexable with dates than I can suggest a cruise which takes off from Istanbul.

If you tell me your dates you can take a cruise sail to Aegean, stay couple of days in Mykonos and return with the same cruise back either to Istanbul or to Kusadasi.

There are many cabin option and reasonable prices which includes full board on the ship.

Happy travelling,