Why would they need to flush the water? If they did, and it's not coming into contact with any major contaminants, why couldn't it go more or less directly back into the water supply after maybe a trip through a treatment centre?
For that matter, wouldn't it be even more efficient to use something like seawater? They are on an island after all.
There's no reason it needs to. If you put some copper sulfate in the water it will keep the microbes at bay and allow you to re-use the water either indefinitely or very good approximation. You could also make a strong brine which would prevent microbial activity and also lower the freezing and melting point allowing you to move more heat with less water on the air conditioning side. It might make your chillers for making ice less efficient, though.
For that matter, wouldn't it be even more efficient to use something like seawater? They are on an island after all.