Jo mentioned strengthening the forearm muscles...and thats important if you are just beginning this type of sport..but i think most of us have been at it for awhile and maybe have been windsurfers before etc.
I sound repetitive but why not just concentrate on MAINTENANCE..that is, brush your teeth, change your chicken loop line once in a while when it looks ratty, and STRETCH those flexor/extensor muscles every day before you go out and once again before going to bed. If you are in bad shape already make sure to ICE after long sessions for 15 minutes to decrease the inflammation.
The velcro straps sold to decrease the tendonitis can help because it distributes the load of the tendon insertion into the bone over a wider area. But you dont want to become dependent on wearing those and they also can cut off your circulation a bit and they really chafe if you get sand stuck in there between your skin.
again, for those interested the stretch guide at http://www.hotelcaracol.com
shows the commonly used technique for stretching the common flexor and extensor tendons of the forearm.
also, have a look at "hernans" bar that he has at the files section of the Yahoo group. If you are in light winds with a big kite you might want to try this "bungee" fixed loop which will allow you to take some pressure off the arms.
Lastly, dont forget that if all else fails you could try an ARC. I have foils, arcs, and inflos and can tell you that if you kite a few months with an arc the pain in your elbows will DEFINATELY go away!