He should have a gurkha knife, and his handstand move should return. Maybe a variant where he gets a variety of handstand attacks.

As one of the most forgettable and inconsequential characters in the entire franchise, Kai would need a significant makeover. The new timeline gives him ample opportunity to become something new, because he can no longer be a student under Liu Kang.

Hence, new origins possibilities:

Shirai Ryu - the new Shirai Ryu under Master Hasashi took in orphans of the Netherrealm war and trained them. Kai could potentially be a Shirai Ryu. Unlike Takeda, who is splitting his loyalty between Special Forces and Shirai Ryu, Kai could potentially be fully invested in the Shirai Ryu. This falls in line with the theory that Fox was Kai, but since the comic has practically nothing to do with the MKX story, that could change.

Black Dragon - Without the guidance of Liu Kang and the White Lotus Society, Kai could have instead been influenced by the likes of the Black Dragon, joining Kano, Jarek, Tasia, Tremor and the others.

Red Dragon - Again, without the guidance of the White Lotus, Kai could have been influenced or possibly abducted by the Red Dragon when his potential was identified by Daegon. Daegon could be systematically removing future threats from Earthrealm by indoctrinating them into the Red Dragon, and Kai could be one of his chosen. Hopefully, if at least some aspects of the comic are true, Hsu Hao and Mavado are dead. Kai could take one of their places.

White Lotus under Fujin - With Raiden going "dark" and possibly corrupted by Shinnok's essence, and with the numbers of Shaolin Monks significantly dwindled due to the loss of Kang, Lao and the Netherrealm conflict, Fujin would have no choice but to reform the Shaolin and select warriors from around the world to represent the White Lotus. Kai could be one of them, and this would fall in-line with his original story...if there ever really was one to begin with.

There's a lot of emphasis on his "handstand" ability, but it wasn't really anything more than a kick. He was basically a watered down Liu Kang with his fireball and Shaolin backstory. He could essentially replace Liu now as his "good" counterpart, utilizing more Shaolin techniques rather than the dark powers Liu now utilizes.

I expect Kai to be taught by Fujin or Shujinko's reformed White Lotus Society.

The comic has nothing to do with the game's story because it's a completely different story taking place somewhere inside the 25 years period of MKX. The story is basically . It's not mean to be an MKX tie-in or an extension of the game's story. It's its own story within the MK Universe, featuring characters that didn't make it into MKX and a first look at the "kombat kids" and what they did prior to MKX.

...but with so many continuity errors that it can't possibly even tie in to the overall game story, not just MKX.

Sorry, but I don't buy into that at all. The comic book is called "Mortal Kombat X" and it was touted as a tie-in backstory to the game which has the same name: Mortal Kombat X. What we got was a disjointed mess of continuity errors and story elements that had absolutely no bearing on the overall Mortal Kombat franchise, because none of it mattered or had any impact. The only thing that translated over to it was the fact that Scorpion took in Takeda for Kenshi. The end result is Mortal Kombat X the comic, and Mortal Kombat the game series. Neither are tied to each other. The comic has about as much to do with the game series as Green Lantern does with the Independence Day film franchise.