Can my Alakazam be a dragonite killer?

Well.. it is possible, after all his ATK is pretty huge and DG deals extra damage to dragons, but ice types are A LOT better, Piloswine with powder snow/avalanche seems to do an awesome job, or any other ice attacker. Dragonite has double weakness to ice

You are going to have to do allot of dodging due to the glass cannon he is.

It's possible.

(I wasn't sure on your mon's CP so I just put 2500 vs a 3000 dragonite with DT/Hurrican)
https://www.pokebattler.com/fights/attackers/ALAKAZAM/quickMoves/CONFUSION_FAST/cinMoves/DAZZLING_GLEAM/cp/2500/defenders/DRAGONITE/quickMoves/DRAGON_TAIL_FAST/cinMoves/HURRICANE/cp/3000/strategies/DODGE_ALL2/DEFENSE_RANDOM

Dodge All had the best results, but he can survive by using any of the Dodge All strategies, and could come out with a sliver of life on Dodge Specials PRO. Explanations are in the question box to the right of the selector (just click on the top left menu, go to battle, then to the right of the Attack Strategy the ? will explain the tactic).

Gengar is also pretty strong vs Dragonite. My 2235 SC/SB took out 2 3k Nites today. SC & SB have crazy good DPS and SC is so fast you can dodge everything keeping Gengar alive for a long time.

Otherwise the better ice monster: Cloyster, Piloswine, lapras can take out 2

I have a maxed out zam that used to be able to take out around three 3000+cp dragonites with sw quick moves before the gen2 changes. Has pc/p but supposedly now confusion better?