Please note that your arrival in Athens airport needs to be in time to transfer to the domestic flight to Kythera. You need a recommended two hours to transfer. You may need to stay in Athens for a night. If you want to arrive on Kythera a day or two early, just me know. Or, for a long wait in Athens Airport, you can find Athens Airport Lounges here. Access to use of a lounge is about £20/£25.
Below is a search on Sky Scanner on Sunday 1st September.