I've ridden both SUP and longboard with a kite and it's pretty important that the water is relatively flat to make it fun. If it's choppy you just kind of slap the nose of the board against waves and you can't maneuver the board well enough to avoid the waves.
If you have a decent ground swell coming in a long board might be fun if the wind/wave angle is good. If it's onshore though it wont work as since you are on a long board that probably means 10 knots or less of wind so once you start moving in the wind direction in that light of wind the kite will need constant looping or it will drop and if you are looping the kite you aren't really riding the wave.
Now if you have cross shore winds or offshore winds (and a bay on the ocean side for safety) it can work well. Normally though the sea breeze will be dead onshore.
Here is a video of me trying to ride an 8 foot Wave Storm in onshore chop:
https://youtu.be/1DZa-oK50ws?t=260
If I was choosing a board to do it on I would probably go with Lib-Tech pickup stick 7-6, only 53L of volume though:
http://www.lib-tech.com/surfboards/pickup-stick-7-6/