I was there beginning of july 2018 during 2 weeks. Great holidays
For kitesurfing you need to go at the end of the psalidi beach (east side, "windsurf & Kite surf kos windzone" on google map https://www.google.fr/maps/place/windsu ... 8883?hl=fr
There is a Club https://www.windzone-kos.gr
where you can rent RRD Gear and you can take lessons (there are 3 teachers , very nice guys like the owner George ).
For the wind forecast you can check it on Windguru https://www.windguru.cz/501259
, it's not really accurate but it can give you an idea .
Water is not flat especially when the wind is strong , waves are coming from north west but it can be fun to jump or to "surf" when you come back.
Beach on the kite spot is a pebble beach, i was wearing shoes so it was not a problem for me but some guys were kiting without shoes so it's up to you.
https://firstname.lastname@example.org,2 ... 6656?hl=fr
The picture has been taken during the winter so you cannot see the club.
At least , don't forget to go to eat at the taverna "Nikos & Kontessa" https://www.tripadvisor.co.uk/Restauran ... egean.html
We eat there every day for lunch and it was perfect.
If you have questions don't hesitate.