There are at least three that I counted. Some are more informal.
The two times I was there I watched these guys operate:http://www.srilankakiteschool.com/
They ran a pretty good operation and their students appeared to learn quite well. They have a very small lagoon that is nice and shallow in some parts that is very conducive to learning. The area is small so over the course of three days I watched the students progress and was impressed with it.
The small flat water lagoon is great for intermediate and experts as well. It really forces you to just practice the same trick over and over again until you nail it. On the other side of the beach is the ocean and you can have some pretty good waves there with miles of empty beach. It's really an ideal place for kiting.
There operation actually has vehicle transportation to and from a small complex they have built and they cater for you at around 50-60 euros a day, which although steep for the region, is probably worth it if you aren't on a backpackers budget. Each time I went, I came last minute and they were fully booked.
Sri Lanka has very little tourist infrastructure in this area, so basically if you just show up at that lagoon you will find almost nothing there. So you need to book with them ahead of time. Otherwise you'll need to find a willing family to take you in etc. It's a bit complicated. I ended up staying at a resort that cost quite a bit more.
This time of year January- March is the off season. There is not a ton of wind, but since you are local you can probably arrange with one of the local instructors for something when the wind picks up. One of the guys is a regular on this forum and he's really helpful. His name is Dilsiri. http://www.kitesurfingsrilanka.com/
I'll probably see you there starting next Monsoon. In the mean time, you might consider hopping a flight to Thailand.