Hey,
I've seen and heard people do actually kitesurf in Singapore - East Coast Park and near Changi. I've also heard from various sources that kitesurfing is banned in Singapore but then have heard conflicting reports that it hasn't. Although as far as I'm aware there is no-one that you can learn to kitesurf from here.
When I first moved here I researched into it as I had done a basic course in the UK and was eager to continue. The only site I found was:
http://www.kiteboarding.com.sg/
It wasn't very up-to-date (and now is even less so), and it stated that the training was actually done in Malaysia (and you would have to make your own way there).
Other places I have found are::
Bintan
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Unfortunately when I went there it was the "off-season" and they had no wind, therefore the instructor wasn't there at the time. The resort I went to, Mana Mana, has since got new management and they have moved all the water sports to East Coast - minus the kitesurfing:
http://www.manamana.com
Bali:
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Again I went there in the off-season (according to the instructor the worst month for wind - how was I to know?), but they seemed friendly:
http://www.bali-kitesurfing.org/kiteschool.html
Thailand:
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http://www.kiteboardingasia.com/
I've also heard there are places in Vietnam to learn but are more difficult to get to.
Let me know if you're planning a trip or find someone in Singapore to teach (I have my own equipment) because I am still keen to get out there on the board.