My Kukulkan arena build

I don't think Hide of the Urchin is really all that useful in Arena; I'd swap it out for either Magi's Cloak against a CC heavy team or Mantle of Discord for helping you escape if you're being targeted by the enemy assassin (especially Loki and Ao Kuang who can sneak up on you).

Book of Thoth is great on Kul and on, but you'll want to be able to stack it quickly and that's not always possible. One thing you do not want to do in Arena is compete with someone else who's stacking because there just aren't enough minions and gods to go around. I'd skip it if it looks like my team will pretty much insta-clear a wave or if someone else is stacking because it's not really worth the price unless it's fully stacked.

Soul Reaver and Rod of Tahuti are situational items with the former only being useful if there are two or more enemy gods building over 2k health and the later if you can hit your ult regularly, which isn't always easy in Arena due to the wide open space.

As stated below, you need some type of pen before your 4th slot; a good item is Divine Ruin if the enemy has a healer or two or more gods with self-heal like Hercules or Vamana. Spear of the Magus is a good pickup for its flat pen and protection reduction, especially if you can consistently hit your Whirlwinds. You can skip Magus and get Obsidian Shard forth if you're dealing with 2 or more tanky characters, though I would probably get DR 3rd. Spear of Desolation can work as well, but's fairly expensive and you have to keep in mind the 40% cooldown reduction cap.

Chronos' Pendant is nice, but it's expensive and Potion of Magical Might gives you 10% CDR. Yes, you should be able to afford it after your build is finished.

A couple of situational items you didn't mention:

Shaman's Ring: Good power for a fairly cheap price and its passive is easy to stack.

Polynomicon: Sure Kul's not really an AA mage, but Poly has power, mana, life steal, and its passive is fairly easy to use after you've used whirlwind or Zephyr.

Gem of Isolation: Yes it's a cheese strat, but it exists and there's usually no reason not to take it. Bedsides, the health and CCR do help out a bit.

Book of the Dead: If you're building Book of Thoth, you should build this as well due to its power, mana, and passive.

Soul Gem/ Pythagorem's Piece: Both of these essentially serve the same function, but gem has the potential to do some serious burst damage if you can hit your abilities. Add in the lifesteal for keeping you alive while retreating or letting you stay out longer for more XP and gold, plus the CDR makes this a good pickup after book or in place of book if you don't think you'll be able to stack it quickly.

I mean usually if you're getting Spear of Magus it's your 3rd/4th item, not something you consider 5th.