Shadow Dragonite

As a Pokemon with high attack, Dragonite greatly benefits from the Shadow Boost, becoming one of the absolute strongest dragons in the game. It's very comparable to Shadow Salamence, but it has a little bit less DPS along-side a little more TDO, just like the interaction between the normal versions of these pseudo-legendary Pokemon.

Best PvE Offensive Moveset

• Dragon Tail slightly outperforms Dragon Breath in damage output, but Dragon Breath is easier to dodge with.
• Steel Wing has a different effectiveness profile but is inferior for neutral damage.
• Outrage deals huge damage and has 2 bars, with its drawback being long cooldown. Dragon Pulse is strictly worse.
• Draco Meteor*, Dragonite's Community Day move, is competitive with Outrage, but being a 1-bar move is less consistent. 
• Dragon Claw is great for clearing gyms with 3 bars and low cooldown, but trails Outrage in damage output.
• Hurricane gets STAB but lacks synergy with Dragonite's fast moves. 
• Hyper Beam and Superpower have no purpose on an offensive Dragonite.

Best PvE Defensive Moveset

• Dragon Tail performs exceptionally better than all other fast moves on defense.
• Steel Wing is acceptable on defense, with advantages vs. Ice, Fairy, and Rock.
• Dragon Breath is underwhelming on defense.
• Dragon Claw fires quickly and often, so it’s hard to dodge, but its power is low.
• Superpower has great counter-coverage against Steel and Ice Types.
• Outrage has stellar power and 2 bars but is easily reactable. Dragon Pulse is strictly worse.
• Hurricane is difficult to react to, but Shadow Dragonite may likely faint before using it.
• Draco Meteor* has strong STAB damage, but is easy to dodge. 
• Hyper Beam has no redeeming qualities on defense.

Following the GBL Season 8 update, Dragon Tail on paper is slightly stronger than Dragon Breath, but the latter is much easier to use and benefits significantly more from certain breakpoints. Steel Wing is a poor move. 

Dragon Claw is mandatory for its cheap energy cost and solid damage. You have some freedom in secondary charged moves, though you do spend most of your time just spamming Claws.

Draco Meteor is the most extreme option, giving an incredibly powerful nuke in shields-down scenarios. Outrage is less hard-hitting than Draco, but also less punishing if it gets shielded. Hurricane is really nice because it actually gives you a way to damage Fairy-types, though its energy cost makes it inconsistent as an actual answer. Superpower* is the most likely recommended move for Dragonite, giving it an option against common Steel-type Pokemon, in addition to its other weaknesses against Ice and Rock Pokemon. It should be noted that without Hurricane, Dragonite has no answer to Fairy Pokemon at all, but Dragonite wouldn't typically win in a one-on-one fair fight against Fairy Pokemon anyways.