Kini beach is 9 km from the port of Syros and also from the airport.
From the port of Syros you can come to Kini either by car or taxi (10 min) or by bus (the starting point is at the port of Ermoupolis, next to the fire department, duration 20min).
From the airport you can take a taxi (10 min).
From the port : https://goo.gl/maps/7u8dFWFLsNczXUV18  
From the airport : https://goo.gl/maps/gtesCFVWK7mpDbqx8