Let's talk Kukulkan.
Kukulkan boasts high area damage and devastating burst. At max rank, Spirit of the Nine Winds deals a massive 900 +120% of your magical power in magical damage. That's the kind of ult that makes squishy targets disappear.
The tight spaces of Season 5's jungle let's Whirlwind shine as a zoning ability. With great wave clear to rival Poseidon's and the potential to turn entire corridors into death zones Kukulkan makes for a decent mid laner.
Kukulkan can get an enormous amount of power with his passive Power of the Wind Jewel in combination with the passive of Book of Thoth adding 8% of your total mana pool to your magical power. He gets on very well with the Spellbook library tree of magical power and mana.
The main downside is that without a dash or leap and little self peel he can be very vulnerable to gank attempts. That said, Slipstream does allow him to juke well and get around the map quickly.
8% Mana conversion into Power can make quite a bit of difference to your item choices compared to other mages. I've included the bonus when talking about the power that items provide.
Starting with Book of Thoth is highly recommended for the large amount of power and excellent synergy with your passive. At full stacks, it gives you an enormous +170 Power on its own, without considering the rest of your mana pool.
Shoes of Focus offers a fantastic 60 Power, 250 Mana and 10% Cooldown Reduction. Even so, the more expensive and lower power Shoes of the Magi is my personal preference because the Penetration gives you slightly more damage against enemy gods which is nice to get early.
Cooldown Reduction is important for Kukulkan, which makes Chronos' Pendant an excellent 3rd item pick up, especially if it's your only cooldown item. If you got Shoes of Focus I'd recommend Spear of Desolation instead. That is a higher damaging option, but don't forget that Chronos' Pendant provides very useful mana sustain.
Gem of Isolation is an excellent pick up that adds a great deal of control to the kit. Whirlwind becomes a long lasting mass slow and Zephyr all but stops people from moving, which is great for setting up Spirit of the Nine Winds. The control combined with the additional health offers a decent improvement to survivability.
Simply put, Spear of the Magus works brilliantly with Whirlwind and otherwise greatly increases combo damage vs. squishy targets.
Polynomicon and Kukulkan is a match made in heaven. It offers +99 Magical Power and the Lifesteal improves your quality of life with health recovery. The passive is the star of the show, adding massive burst to your basic attacks after using any ability. This is especially nice for resolving the awkward downtime that Kukulkan can have after using his Whirlwind.
Finally, Soul Reaver grants +154 Power and great bonus burst damage, particular against high health targets.
Warlock's Staff is undeniably a great item that starts off with decent stats and grows to be a bit bloated when fully evolved. Choosing this first greatly improves your ability to survive, but can significantly delay your power coming online compared to Book of Thoth. Double stacking is an option; Book of Thoth is not terrible to get later on in your build because even without stacks you'll get a good power boost from your existing mana pool.
Obsidian Shard vs Spear of the Magus is an interesting choice that depends on the situation and your priorities.
Obsidian Shard offers less against targets with low protections, but its effectiveness against tanks may increase your impact against the whole enemy team. Although Obsidian Shard doesn't have the same synergy with Whirlwind, it is good for one-off shots of your 1, 4 and poly procs. Note that Spear of the Magus's protection reduction helps allies' magical damage too. Especially later in the game Obsidian Shard can be the better choice.
Late game Slipstream has you speedily slithering all over the place. It's such a good movement ability that you can trade out your boots altogether, but I do like to hang on to movement speed for slippery juking. Shaman's Ring makes for a strong replacement that adds lots of damage (you'll stack the passive no time in the late game).
Other potentially good (situational) options: