In Kingdom Hearts there are few cutscenes I think that give hints toward Sora's and Kari's relationship.In Port Royal while Will and Elizabeth hug Goof and Donald noticed Sora's face is turning red,then Donald says "Aw I know who you're thinking about".Also in Halloween town while Jack and Sally dance Sora sees himself dancing with Kari. https://m.youtube.com/watch?v=6njjNMPQ-MA 2:08:42 in Port Royal.

Yep, I always noticed those, and even beforehand, you could see hints at a special connection between the two. Arguably, the game that establishes this fact the most strongly is Chain Of Memories! With Namine hinting to Sora what's most important to him, the person he could never replace, the girl who's special to him, his light in the darkness; it all just adds to the fact that Sora and Kairi do indeed have a strong bond that could end in them being a couple by the end of Kingdom Hearts III!

It's been telegraphed since the beginning of the first game that Sora and Kairi liked each other and it only intensified after the first game. I know people focus on Sora and Riku to satisfy their need for yaoi pairings but it's been obvious from the first scene on Destiny Islands that Sora and Kairi cared about and were interested in each other.

 

I've always believed that Kingdom Hearts III will be the 'culmination' of this relationship teasing. Whether they actually kiss or not, who knows.

It's been telegraphed since the beginning of the first game that Sora and Kairi liked each other and it only intensified after the first game. I know people focus on Sora and Riku to satisfy their need for yaoi pairings but it's been obvious from the first scene on Destiny Islands that Sora and Kairi cared about and were interested in each other.

 

I've always believed that Kingdom Hearts III will be the 'culmination' of this relationship teasing. Whether they actually kiss or not, who knows.

 

I know!!! Like I mentioned earlier, Chain Of Memories is the game that most strongly emphasizes on Sora and Kairi's relationship! I am looking forward to seeing how they evolve from what has been set up so far!

Isn't that obvious since the beginning of KH1 on Destiny Island?

it's definitely been there from the beginning, but honestly i'm glad they never really dove into a romantic relationship between the two of them. i don't think the series would be able to handle a bad romantic subplot. it's better to keep it unspoken imo

There's also one scene in the prologue of KHII where Roxas talks with Kairi for a bit, referring to her as "that girl [sora] likes." 

 

Isn't that obvious since the beginning of KH1 on Destiny Island?

Of course it is, it doesn't stop a big part of Soriku shippers going to try and deny all obvious hints and instances every turn they can while over-exaggerating every single Sora-Riku interaction themselves, though.

I already made a list like a week ago or so of hints towards Sokai in KH2:

 

• Sora takes out Kairi’s good luck charm and looks at it wistfully (at least two times since it changes pants pockets between Twilight Town and the epilogue)
• Sora imagines himself dancing with Kairi when he sees Jack and Sally dance (plus super cute in-love-and-flustered chuckle)
• Donald and Goofy tease him when Sora watches Will and Elizabeth, that he’s thinking about her and blushing (and since he later imagines himself dancing with Kairi, it's obvious he's thinking about her and NOT about Riku)
• Donald comments on how Kairi would find Lion cub Sora adorable (of course she would, he was freaking cute)
• Olette comments on how romantic Kairi’s story is
• Sora literally BEGS Saix to lead him to Kairi
• they finally hug in an intimate way (Sora leans in, closes his eyes; even Donald and Goofy are happy/embarrassed to watch this touching moment)
• they promise to always stay together for Roxas and Naminé
• Kairi’s letter - Riku immediately hands it to Sora, knowing it's for him and it helps Sora open the Door to Light
• Sora looking fondly at Kairi’s addition to the cave drawing

That's what I could think of of the top of my head, Roxas talking about Kairi as the girl he likes has already been mentioned here. And yeah, that doesn't count what happened in KH1 (although understandably toned down a lot and still more in a friendship way than a romantic way) and especially in CoM.

 

I know that it's been toned down in the later games, but really, there wasn't a place for those feelings in Coded and Dream Drop Distance anyway.

Coded was about Data Sora from KH1 and Dream Drop Distance had Sora and Riku knowing that Kairi was safe back on Destiny Islands. They could've shown him missing her, but seriously, he was there on a mission and he knew it wouldn't take that long. Also, in Blank Points, he basically asked for her permission. He made up his mind, but he was really hesitant about telling her, afraid of her reaction. He wouldn't be if he hadn't been afraid to hurt her feelings.

 

So yeah, there's tons of stuff hinting at a Sokai ending (or at least initially planned Sokai ending). Oh and let's not forget the 2.8 ending montage of the Disney Couples that so conveniently ended with a 30s-1min Sokai montage. They're still hinting at them.