I have been recently to the island.
Wind season is late december to June. Right now is hurricane season..which means lots of rain and no wind. Due to hurricanes on the atlantic, the wind direction will also change (which is not good for kiteboarding).
This year they have (just like many caribbean islands) a huge/big/ epic stinky sorgassum problem.
All kite beaches and bays are still covered in epic amounts of stinky sorgassum.
At the moment they are cleaning it up..But that proces goes veryyy slowly.
I think that at the beginning of 2019 the situation will be back to normal (just before the high tourist season begins).
The winds are never strong by the way. 21-23 knots is the absolute maximum. But 15-20 knots is more likely on a very good wind day. I would say Brazil is the Nirvana for its consistent wind but not Martinique.
Here a link to follow the sargasses problem:
La pointe Faula is the most acces-able spot and the main kiteboarding spot. Which can be veryyyy busy when its windy. It has a tiny lauch area. You have to roll up your lines every time you come in for a break due to lack of space. But once on the water its okay.
Accomodation: There is lots of choice....depends what you are looking for. I would say stay somewhere along the east coast, that where you will be kiting.
But most important is to rent a car. without that you can't go anywhere.