Singapore has two periods... the SW monsoon and the NE monsoon. in between these monsoons are often erratic wind and thundershowers (can be big, can be small, can be none).
the SW monsoon is weaker (5-12 knots) and dominated by "sumatrans" or little squalls that spin off of the Indonesian archipelago. its ok for windsurfing as a diligent sailor with a LOT of time to watch for wind can see the storms coming, rig up and maybe get 30-50 minutes of wind every few days as fronts roll through. once the rain starts, the wind drops. so this monsoon sucks for kiting. yeah this is not the Gorge.
the NE (actually usually NNE) monsoon is a short season (Dec to Feb) and generated all the way from continental Asia and works its way down the South China sea and influencing the SE Asian coast (eg Vietnam and Thailand will have a longer season as this monsoons influence works from North to South). in Singapore it hits our NE coast and thus the best place to kite during this monsoon is a little carpark at the end of Changi runway (i think the road is old Nichol Highway, the one way at the far east of Singapore). its a good place though planes taking off overhead might freak you out.
the problem is that this is part of the narrow ocean straight that seperates Singapore from Malaysia and there is dense boating traffic (im talking BIG ships). i think marine police have relaxed a bit over the last couple of years and they turn a blind eye as long as you do NOT stray into the shipping lane. i'd estimate this is about 300-400 meters off shore. not so far for windsurfing, but quite ok for kitesurfing. during the windy season (NE) there is almost always a dedicated crew of sailors there all afternoon (most of whom probably should be at work). there is a nice little beach, and the wind is side-on shore.
the problem with kiting on Singapore's East Coast, which has been recommended on this thread, is.... beaches are shallow so you will face on (slight side) winds during the SW monsoon.... and the wind dies erratically. during the NE monsoon, the East Coast Park side of Singapore is mostly leeward. the exception is the two most easterly sailing centers.... Peoples Association Sea Sports Center (there is a decent kite and windsurfing shop here), and the National Sailing Center.
Unfortunately, the clean wind during the NE is still about 200 to 500 meters off shore. fine for a windsurfer but a problem for a kiter (there are no water taxis). at the shore, you might find there is actually NO wind! and you might see a very clear wind line about 200 meters or so off shore. reach that and you are blasting. the really clean wind here is >500 m off shore.
the NE monsoon can blow consistently 15-25 knots for several day cycles. its good and occasionally choppy. no real waves.
what is a good kite size? i would say the biggest kite you have (eg for 80 kilo kiter, 14m or 16m bow) with good depower and a wide board. for a windsurfer, you will get mileage out of >9.5m sail during both monsoons and i liked a 7m sail during the NE monsoon.
ok. whew. now for other places....
Bintan is a sleepy little island not far from Singapore. the beach there is ok and catches a good amount of the NE monsoon. when its 15 knots in Singapore, its probably 20 knots in Bintan, side on shore (45 degrees). problem is that its a bay, not that wide, and choppy so it would be tough to learn there... as upwinding on a kite is one of the skills you surely will not have at first!
i know that there are many good places in Malaysia (Kuantan, but no rental or school), Thailand (hua hin etc) and Vietnam (ive never been but hear its great).
i only have first hand knowledge of Bali (S Sanur, Metarsari area). July and August see good side-on winds there (70%? days 13-22 knots?). its good consistent wind and a big BIG bay with flat deep water and about 1km out, there is big Bali surf. in Sanur there are two main schools/locations for kiters.
Blue Oasis (Bali) is a nice beach with grassy area and run by a Italian named Mario.
Bali_KiteSurf is about 300m south of the Mercure Hotel and is a more rustic beach, with a little van (Komang and Kadek, brothers). This school is cool too, and less touristy and way more laid back. both are decent places to learn.... and i know that they sell kites (Komang and Kadek). you can even get a water taxi to the clean wind (50,000 IDR, about 5 usd). that makes it a LOT easier to learn when you get watertime.
lastly you can try Boracay, a beautiful jewel of an island but not so easy to get to. very strong winds at times (15-35 knots), on shore. it can get very busy (eg 40 kiters?) so not great for beginners. i ended up just windsurfing last time i was there.
so... Ninocamino, i would certainly bring your kit esp if you intend to travel at all in Asia.... its fine. Singapore sort of frowns upon kiting but in the end, know the local tolerance, and i think you'd get more than a few days in during the NE monsoon.
for the guy going to Bintan in Sept... i think very unlikely you will get wind. Bintans season is roughly the same as Singapore's.