Whats a good move set for dragonite?

A Dragonite does not learn Dragon Claw naturally, but I think he learns Outrage at Lv. 65, me personally, I don't like Outrage, I don't think that it's a good move, much less a good Dragon Move.
But, I think that a good moveset for a Dagonite of the Advanced generation would be:

Dragon Claw (To keep the fellow Dragon Types at bay)
Flamethrower or Iron Tail (To melt or smash the ice types that come your way, and to flame broil a few other types, and Steel is Super Effective against Ice types, this will allow you to bypass the other types of all Hybrid Pokemon out there)
Thunderbolt (Electric is a good type, plus, a majority of the Ice types out there are hybrids, more specifically Water/Ice type hybrids)
I think that Wing Attack is a good move, and Thunder Wave is also a considerable move, Dragonite is already a fast Pokemon, and Thunder Wave will assure his/her first strike, good moves to have until Hyper Beam comes your way at Lv. 75.

CrystalTitan1, out!

This is what I would have...

Earthquake
Ice Beam
Arial Ace
Dragon Claw

It doesn't learn Dragon Claw this is TM 02 (Found on Victory Road.)
Outrage- lv. 50 Dratini**** lv. 56 Dragonair**** lv. 61 Dragonite
Hyper Beam- lv. 57 Dratini**** lv. 65 Dragonair**** lv. 75 Dragonite

Hope this helps.

Teach it:

Dragon Claw
Sword Dance
Earthquake
Thunderbolt

Personally, I would chose these moves.

Dragon Rush. It Dragonite's special move and it is one of the 7 pokemon that learn it during leveling up, and it is a very powerful move, guaranteed to KO or or lower HP very quickly if you fight a Dragon pokemon your level.

Dragon Claw. It's one of those backup moves if you get tired of using Dragon Rush or run out of PP for it.
or
Outrage. Even though this causes confusion after the user uses Outrage for 2 to 3 turns, it is still a very good move to wipe out an opponent's team.

Surf. Dragonite, even though water doesn't effect it much, can learn water-type moves. This is a very huge advantage over rock type pokemon (one of Dragonite's weaknesses)and fire types as a bonus.
or
Thunder. Amazingly, Dragonite is only x1 affected by electric type moves even though its a flying type. It can also use electric type moves. So, if you already used your Thunderbolt TM, Thunder is a great substitute. It has less PP and accuracy, but it deals more damage.

Fly (or Areial Ace/Wing Attack). Fly is another great move, and so are Areial Ace and Wing attack. You should have only about one flying type move in your arsenal, because there are still room for some other good moves. I would only choose at least one flying type move because you can easily KO fighting type pokemon.

I hope this helps,
A Dragonite Fan.

Noob, how you could say sufr is a good move? Best move for Dragonite are physical moves (because attack is the best stat, not spec. Attack). So best use have Earthquake, Outrage, Fire Punch and Brick Break. For defense against other Pokemon you can choose thunder or flamethrower, but do do not Surf please.

For me I agree. Dragon rush is useless

Keep in mind that 'Physical' and 'Special' moves are, for Fire Red/Leaf Green, determined by type: Physical: Bug, Flying, Fighting, Ghost, Normal, Poison, Steel, Ground, Rock. Special: Psychic, Fire, Grass, Water, Electric, Ice, Dark, Dragon.

I'll be answering ONLY FOR Firered (Gen III).

[b]Whats a good move set for dragonite?

Honestly, it depends on the rest of your team. Dragonite learns a wide variety of moves and depending on which Pokemon you have in your team, you can teach it different moves as coverage. So I'll share with you a general moveset:

[b]Moveset: Standard Moveset
This is a pretty typical moveset for a Dragonite, regardless of trait, nature or other variables.

But if you must:
Dragonite @ Persim Berry
Trait: Inner Focus
Nature: Adamant (physical sweeper)/Rash or Modest (special sweeper)
EVs: 252 Atk (physical sweeper)/ 252 SpAtk (special sweeper)/ 4 Hp

- Outrage/Dragon Claw: Personally I prefer Outrage, because it really utilises Dragonite's raw power and has a slightly higher base power, and it's side effect (confusion) can easily be solved by giving it a Persim Berry. However since all Dragon moves are considered Special in this gen...

- Thunder/Thunderbolt: Coverage, low accuracy but high base power OR high accuracy but slightly lower base power. Keep in mind that Dragonite doesn't get STAB with this so personally I would pick Thunder. But it's up to you.

- Flamethrower/Ice Beam: Coverage, especially for Ice types. Personally I don't like Ice Beam since you would need a Surfer on your team so whichever Water Pokemon you pick (which is highly likely) would be able to learn Ice Beam anyways. Chances are, the Water type Pokemon is a dual Ice-Water type, for instance Lapras, Dewgong, Cloyster)

- Aerial Ace/Fly: STAB and are just convenient moves to have. Aerial Ace is definitely better in this gen since Fly only has base power 70 BUT takes two turns to execute, though Fly is just a good move to have to well, fly around the island.

ALTERNATIVELY: You may kick out one of the moves above (though hopefully not a Dragon type move) to give way for Earthquake: high accuracy, high power, decent PP, a great move overall and one of my favourites. It provides coverage and tackles Electric types, one of Dragonite's weakness as a dual Dragon-Flying type. If you would like to kick out anything I would choose Flamethrower/Ice Beam personally since Dragonite has a 4X weakness to Ice types so... Just RUN if you ever meet a high-level Ice-type since it would be likely to OHKO you. Switch out for a Fire-type (easily obtainable with the game and with strong candidates such as Charizard (my Starter!), Growlithe, Ninetales etc)

When does it learn dragon claw, outrage, and hyper beam?

Dragon Claw: It cannot learn it by leveling up, but you can obtained the TM02 at Victory Road. The HM Strength is required if I'm not mistaken.

Outrage: Dragonite learns it via leveling up at Level 61. If you had a Dragonair, I would have advised you to stop it's evolution since Dragonair learns Outrage at Level 56, just one level after evolving. But since you have already evolved it, it's too late to change it.

Hyper Beam: Dragonite learns Hyper Beam by leveling up at Level 75. Again, if you had a Dragonair, it would have learned Hyper Beam at Level 65, ten levels lower. Alternatively, you may purchase the TM for 7500 dollars at the Celadon Department Store. (You've probably seen my moveset above that Hyper Beam isn't included because honestly it's a pretty terrible move in game, and Dragonite doesn't even have STAB with it and is forced to recharge the next turn, leaving it vulnerable to Ice types. It also only have 5PP which, raised to the max, is only 8PP, so I don't think you should waste a slot on it.)