NY kid. Rough street life growing up. Then MK3 happens while he's young. He's one of the few people whose soul
doesn't get sucked up because of its potential (same way as what happened to Stryker) as a chosen Earthrealm warrior. He didn't get involved in the events of the game because he was still young. Hell, he could have even received the Raiden vision about being a chosen warrior for Mortal Kombat but didn't act on it...he would've just been a kid at the time. Maybe even make it so he killed a member of Khan's extermination squad that found him...but was too injured to do anything after that. After MK3's events he has a fire inside him believing himself special when things return to a sense of normalcy after the invasion. He picks up martial arts because he was called a warrior and wants to fight since he was already a violent kid. His story progresses there with how we know it where he's an absolute martial arts prodigy capable of inhuman stuff.
But he's totally amoral. He just wants to fight and hurt people. Raiden's vision and his upbringing, and maybe just a natural bent towards violence, has made Kobra a dangerous person. He's not right in the head. That doesn't mean he's some psycho killer or anything boringly axe-murderer crazy, he just doesn't have the buffer most people have. Like I said, naturally amoral and capable of violence more easily than most. 'Kobra' is not his real name of course...it's just his street name because he has eyes like a snake. Not literally. They're just eyes that are as cold as a snakes. Early on he got flagged as an older gang member as a kid that wasn't right (but that was useful). Maybe his karate sensei even saw it but wanted to try and help him use the discipline of martial arts to help temper that lack of humanity...and Kobra took to it like a fish to water...but it just ended up making him more dangerous.
He gets revived as part of the Elder Gods gambit...and being an Earthrealmer, gets lumped in with Cage and the SF who are VERY wary of him since he's a Black Dragon...and Kobra could even point out that he doesn't really care about the BD one way or the other. It's just something to do and it lets him fight people. I'd also have it so he's a fan of Cage's movies. Grew up loving them because of all the fight scenes. Give Midway Johnny some immediate growth there as he kind of likes the kid because he's an arrogant punk a lot like Johnny was when he was younger...but Johnny had A LOT growing up which allowed him to be trained all around the world and be a young celebrity and then movie star where-as Kobra grew up with nothing and has gone down a bad path. Start showing that paternal side to Johnny where he has a good heart that we got A LOT of (to good effect) in NRS stuff. He thinks Kobra has just had a bad break and had his talents put to bad use.
Then you create friction with Jax who is older and wiser and has "seen guys like this kid in the military". People that want to serve because they could never make it in regular life...because they just want to hurt people. Jax could point out that people like this NEVER end up making it far because there's something wrong inside of them. Jax doesn't trust the punk at all.
Then narratively you put Sonya in the middle. She respects Jax's opinion and naturally hates the Black Dragon...but her focus is on fulfilling the mission of saving the realms and, eventually, finding Kano to bring him to justice. Kobra is useful for both those things. She's also swayed by Johnny's attitude towards Kobra because she's developed a bit of a soft spot for Johnny (because the Johnny/Sonya dynamic IS a good one that can be emphasized) and how much less of an ass he is. If Johnny Cage could show he was a VERY good person and a hero,
maybe Kobra can too? Besides, its in the best interest of their mission to utilize him and his skills.
Then you've got Kenshi as the perpetual Midway loner where he's disinterestedin the debate and wants to do what they have to do...and makes it clear if Kobra impedes that then
he will kill him. The indecisiveness of the SF in the matter would be part of what helps Kenshi start to develop into a leader...initially out of pure desire to get things done and stop discussing matters as he's guided by the spirits of the sword to right the realms and stop Shao. He also has revenge against the Red Dragon to think about...and, you know what, Kobra could end up being useful to that too...so Kenshi is keeping that card in his back pocket. After all, there is
no way Kenshi is going to hold the L he took from Mavado without getting his runback.
Now you instantly have a dynamic where Kobra becomes a point of contention between the Earthrealm heroes with points that interact with elements of their characters AND their stories. Johnny wants to guide him, Jax wants to put the rabid dog in a kennel, Sonya stuck in the middle wants to use him, Kenshi doesn't care (for now...). As for Kobra? He grew up running with gangs and then killing other gangbangers and drug pushers for fun. He'll fight for Earthrealm because Earthrealm is "his turf"...and no one, not even Shao Khan, intrudes on his turf without getting these fists.
And you mentioned Kai...which is perfect, because as next-gen fighters, Kai & Kobra should be peers. Which means they're perfect rivals. Even have Johnny remark on that. "I dunno, man. Kobra and Kai? That rivalry has a ring to it" after they end up clashing during the course of the story. Have the Shaolin and Earthrealmers meet up and be on good terms with each other and discuss next moves...meanwhile the two younger fighters Kobra & Kai aren't content with the talking and square off against each other. Hell, someone like Shang Tsung might even ENCOURAGE this and manipulate the situation...and he can play it off as a "test" or some other reason that is actually beneficial to everyone involved (since, again, we're playing up Shang 'reforming' right now)
Kobra & Kai throw down with Kai VERY confident he's going to just beat the punk and Kai VERY confident he's going to literally kill Kai. They beat each other silly to a draw (have cooler heads try to break them up but Shang is like "No. This has to happen now or it will happen later" sorta thing). Neither wins. Kai walks away from the situation having a lot of respect for Kobra because of his talent and toughness...Kobra walks away declaring Kai is now "his best friend"...because he can fight him but can't kill him. Kobra is 100% serious about this. He's never had more fun than fighting Kai. This guy is his PERFECT counterpart/rival. He wants both of them to get stronger..and then they'll fight again and he'll be able to kill Kai then. Everyone not only recognizes that Kobra is sincere but that this is the first time they've seen with a genuine smile...which is even weirder. Even Johnny is like "Yeah, Jax, you might be right. This kid's got a screw loose".
Then that sets up future stories where the Kobra/Kai rivalry is one that will develop both characters. They both grew up in 'war zones' but of totally different styles with fighting as a way of life since they were little. Kai killed and wants to get beyond that and become a better person, and Kobra kills but has no feelings about it at all other than satisfaction with his own skill. The rivalry might make Kai slip into worse patterns of behavior...or maybe it could end up making Kobra a better person if he can see his opponent as a genuine friend instead of just someone to hope to have fun beating to death.
Have a point in the story where Kobra gets hurt to keep Kai from getting hurt with the explanation that if Kai were to die to someone else it would reflect badly on Kobra. He wants to beat and kill Kai fair and square. Make it the weirdest friendship in MK. Have Kai, who has seen a lot of death in his life, recognize that there's something broken inside of Kobra...but that he felt like he himself was broken at one point too and he found the Shaolin and got on a better path so it would be shameful for him to just give up on Kobra and think he can't ever be better. Kai has to prove there's hope for Kobra to be more than a killer or, in a way, he's almost giving up on himself and the path he himself took.
The existence of a Kobra Kai rivalry demands his inclusion
I did some generations for Kobra as well with a focus on black as a primary color to off-set the white you said you liked for Kai, that way their visual style would work as inversions of each other.
