Because almost everything Dragonite can learn are special moves, try this set,
Dragonite @ anything you want
252 Sp. Atk, 252 Spe, 4 HP
Outrage- This attack will serve you well! With 120 base power and the because dragon type moves have the best neutral coverage in the game, it is a must in 3 Gen games for taking care of the few other dragon types around.
Fire Punch- Roast Grass, Bug, Ice, and Steel types today! This is a great move with 75 base power and 100 acuraccy it is perfect against ice types, Dragonites bane!
Waterfall- And with a crashing impact the water fall hit! A great move on Dragonite. It will make sure all those ground(because they usually have rock typ moves) and especially rock type die before they hit you.
Substitute/Protect- And watch them attack to no avail! If you have Leftovers or Shell Bell use Substite, if not then use Protect to avoid damage if you predict a powerful move or priority or simply to annoy your opponent.
This will definitly help you progress through any Gen 3 game!