One of the best places to fly kites in Bangkok is on Sanam Luang, that large field in front of the Grand Palace. The public have been flying kites here for recreation since the mid-19th Century. Kite flying season is from about December until the rains start in about July. The height of the season is during the summer month of April when a strong wind blows from the South to the North. During this time of year there is often a kite festival on Sanam Luang. You can either bring your own kite or buy one once you arrive.
Map showing location of Sanam Luang in Bangkok:
GPS Coordinates: 13.756195, 100.493392