Starter items

Core items

Offensive items

Defensive items

So, after several matches and several builds for Krypto, I have found the perfect items for him.

You start off with Tier 1 Abin Sur's Lantern and 3 Health/Will kits.
explanation : You will need to play very defensive at first so the Will regen and the Health/Will kits will help you a lot in lane if you are focused.

Core Items :
Abin Sur's Lantern Tier 4 : It will help you and your allies maintaining Will so you can push a bit longer. It always helps a lot while traveling in groups. The 400 Will is a beautiful addition in this item and so is the 30 Power Damage. Also Cooldown reduction is a must for Krypto.

Amulet of Isis Tier 3 : It will give you 200 Health and 200 Will and 5 movement speed, also another 10% Cooldown reduction. What is most important about this item is the fact that it will help you and your team mates escape or secure kills because of Mercury's Gift. The extra speed is important at this point. Use it with care and activate Mercury's Gift in the most needed of situations.

Atlantean Royal Seal Tier 4 : 300 Health and +50 Power Damage is also good for Krypto. Since he is using melee attacks he will be targeted most often, and also because he is a controller. Skill Harrier is the most important part in this item. In combination with Krypto's Ultimate or his Bone Trow or even his Howl it will slow down the enemies. Enemies will lose 20% movement speed and you and your team mates can use this to your advantage.

Suit of Sorrows Tier 4 : 150 Health is decent and 50 attack armor is what you need the most, since you will be targeted often. Being a bit tanky will help you escape the most dire situations. and 15% Reflect on attack damage is going to make the enemy think twice before attacking you. You can always replace this item with Metallo's heart and in combination with your E skill (Howl) you will make the enemy lose more attack speed. This is a situation case, because you can pick depending on what your enemy has most.

Mirror Masters Prism : Again 150 Health and 50 power armor. You will need the power armor against the enemy mages. The reflect 20% Reflect on Power Damage is good and it will make you last longer in lane. Again I say this : you need to be a bit tanky because you will be focused a lot, but if you have these defenses up, you can last long enough in order for your team mates to secure kills or objectives against the enemy team.

Gorilla Grodd's Helmet Tier 4 : +15% Resilience, 400 Will and 10% Cooldown are going to help you big time, but what is most important about this item is the Gorilla City Aura that will give your team mates +15% Resilience as well and the Psychic Shield that will give your team mates a shield. This might save their lives many times. You have 1 shield on Krypto but why not have 2 of them? It is definitely a life saver.

These are the main items you need to build on Man's best friend, but wait! There's more!
In case you want you can build some offensive items or defensive ones that will also give you a decent edge. These are items are based on the situation you are in.

Psi Scimitar : +40% will regeneration and +85 Power Damage if your playstyle is more aggressive and you want to chew on the enemies you will need this. The Skilled Attack on this item is definitely gonna make you chew even on the most powerful couch :D .

The Book of Eternity Tier 2 : 60 Power Damage and 35% Power Penetration is again, a good addition for an aggressive play style. It will make Krypto from a little puppy to a feared Dire Wolf that can secure kills itself.

Starheart Tier 3 : If the Book of Eternity made you feared, this will turn Krypto into Killto. 100 Power Damage and +30% more power damage is the bone! See what I did there? Bone, Bomb? Ahh..forget it :D

The next 3 items are situational defensive items based on what the enemy teams composition.
Neron's Contract Tier 4 : +30 Attack Armor and +60 Power damage is not a bad deal. You can definitely sign this contract! xD . Anyway, the good taste in this item is the Blood Bargain. Being invincible for 2 seconds is a great thing even if you are suppressed. You can escape many situations with this specially if you are targeted a lot.

Metallo's Heart Tier 3 : 200 Health, 50 Attack Armor and +10% Cooldown are incredibly good stats. Dampening Aura is a permanent passive in this item and will make your enemies lose 20% Attack speed and in combination with On the Hunt skill (E) that lowers the enemies attack speed again by 30% it will make your enemies attacks as slow as a turtles.

Olympus Gambit : +200 Health +10 Attack armor and +10 Power armor. The health is good enough but the passive in this item is what makes this item. +15 Attack Armor +15 Power armor and +10 Health Regen per 10 seconds for all allies. Lets not forget the Active on this item, Bastion. That will reduce the enemy damage by 25% for 3 seconds.

STOLEN POWERS TIME!
Green Arrow's Surveillance Camera : Since Krypto is a support Cams are a must. Why? Because it will offer you vision in places and will warn you in time if a jungler will try to pray on your lane. You can also use them to destroy the enemies cams because it can see through Stealth. This may offer you an edge if your jungler wants to help you secure kills.

Arcane Green Lantern's Healing Wave/ Krypto's Healing Wave : ArGL's Heal offers you Power Armor and Attack armor and Krypto's Heal offers 35 Heal over 5 seconds. Both of them are very good but I want to tell you why to pick Healing Wave.
Explanation : Early game this will help you and your partner stay in lane a bit longer or help you in the most dire situations. In fights can make the difference between win or defeat. You will need Heal if you want to support your team mates properly because it benefits all of you.

Mods time.

Empowered Amulet of Isis : 35% movement speed for all allies is a good choice on this.
Empowered Atlantean Royal Seal : 25% less movement speed on enemies is again a good choice. Why? Well..you can slow them and your team mates can kill em :D.
Enhanced Gorilla Grodd's Helmet : 200 more Will doesn't hurt at all.

Synergy : I for one have tried only 2 out of these posibilities.
With Blue Beetle it works incredible and same goes for Gaslight Batman. The combo Krypto and these 2 can pull of is incredible.
I don't know about Atomic Joker that much, but I think Krypto can work wonders with most of the marksmen. ^^

This is all I can say regarding this build. I hope it will bring you all overall a greater experience on Krypto and please tell me how it will work. I also take advice regarding my build and I can improve it. Thank you very much for reading all this. Have fun and Bark your way to Victory, Protectors!