Can my floor support Kitchen Island?
The counterop weighs less than 300 lbs. The cabinets probably weigh less than 100 lbs.  This is about 400lbs spread over a floor area of almost fifteen square feet. this is less than 30 lbs per square foot. 

An adult standing still is about 150 lbs on one square foot.

You should have no problem with the load regardless of the placement with regard to the joists.