Kai eggs can be found in Explorations or obtained in the sale (bought or as an extra), and then hatched in the Hatchery.
The Eggs will be lineageless, and they can have any existing trait/element/ability.
A geno rolled from an egg will have 6 markings: 3 are guaranteed to be Common, but the other 3 can be Common, Uncommon, Modifiers or even Rare!
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Kailing geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Kaiyume geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Morikai geno.
Source: Rare Loot (Exploration with Reindeer Familiar)
Use: Can be hatched to get a random Ancient Kailing geno.
Source: Rare Loot (Exploration with Reindeer Familiar)
Use: Can be hatched to get a random Ancient Kaiyume geno.
Source: ???
Use: Can be hatched to get a random La'Kai geno.
Source: ???
Use: Can be hatched to get a random Yakaima geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Umikai geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Walrukai geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Batikai geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Kaiden geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Batekai geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Kaicross geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Lawankai geno.
Source: Winter Event
Use: Can be hatched to get a random Kashi'Kaira geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Kairon geno.
Source: Easter Event / AR Loot
Use: Can be hatched to get a random Cr'Kain geno.
Source: Rare Loot (Exploration)
Use: Can be hatched to get a random Lunekai geno.
Source: AR Loot
Use: Can be hatched to get a random Kaileum geno.
Source: ???
Use: Can be hatched to get a random Tai'Kaith geno.
Source: ???
Use: Can be hatched to get a random Tai'Kaith geno.
Source: Sale / Sale Reward
Use: Can be hatched to get a random geno (any species is possible).
Wait... Is that an egg? How did it end up here?