Some details from the Singapore Kite Association FAQ:
Where do SKA members fly their kites?
Sengkang East Way / Sengkang East Rd vacant field next to CHENG LIM (SW 1) LRT
- West Coat Park CP3
- Vacant field between Punggol Field and TPE
Where to buys kites in Singapore?
Readily available at all heartland stores.
Where to buy materials to make kites?
Try a craft & hobby store : Spotlight
Does SKA fly luminous kites?
Kites are tethered flying objects. It has come to our attention that a local company is marketing remote control flying crafts (fitted with flashing LED lights) with the word "kite" in their product. These objects are NOT "kites" Conversely, if you see a flying toilet seat tethered on a line, this flying seat is a kite.
For rental see here (S$12/d)