Daisuke and Ken, much like the stereotypical red/blue character trope, were literally designed as complements, both in regards to their personalities and their physical appearances. This is most apparent in Diablomon Strikes Back (lovingly dubbed Daiken the Movie), where Daisuke with his maroon-colored hair wears blue and Ken, his hair more obviously indigo than in the series, wears a maroon sweater instead of his typical neutral tones.
Daisuke (Davis) - Bearer of the Digimentals of Courage, Friendship, and Miracles
Daisuke is a ray of sunshine and one of the most genuine characters in all of the Adventure universe. He is always optimistic and eager, even when his team and his family don't believe in him. He refuses to let that bother him, even to the point that he remains unaffected by BelialVamdemon's illusions.
His main character arc in 02 is coming to understand what it means to have a deep friendship, especially the dynamic between two people, the give and take involved, and he never would be able to do that without Ken. But even before he understands what friendship truly means, he is one of the most devoted characters to have ever existed. When you have his trust and affection, he will always have your back.
He's willing to go the distance, to do what needs to be done, even when everyone else is afraid, whether that means facing the Digimon Kaiser and Chimeramon or facing BelialVamdemon. When everyone else thinks the situation is hopeless, he pushes onward because he knows it's the right thing to do.
The team is the most important thing to him. He understands the different members of the group, and he knows how to delegate and utilize every member's individual skills, even if that means he loses the credit for his leadership skills. He puts the group and their partnerships above all else, even when the others don't, even when the group doesn't believe in him. Because you're not just partners with your Digimon, you're partners with the rest of your team as well.
Above all, Daisuke is a miracle worker. He improves and succeeds based on a strange mixture of luck and perseverance. And it's fucking beautiful.
Ken - Bearer of the Crest of Kindness
Ken, though, is the opposite of Daisuke. Where Daisuke is outgoing and energetic, Ken is reserved, quiet, and introverted. Where Daisuke is blunt and open, Ken thinks about his words carefully and does his best to make sure all involved parties are happy.
As the Bearer of the Crest of Kindness, Ken is the pure embodiment of what kindness (yosashi) means in Japanese: He is kind, yes, but he is also gentle, delicate, affectionate, graceful, and sensitive. He is careful and empathetic, and he does his best to help and protect others. He is incredibly sweet and considerate, perfectly polite and able to understand social mores.
However, because of his time spent as the Digimon Kaiser, Ken blames himself for all the things that go wrong in the Digital World, and he is determined to fix all the problems he created, even to the point where he's willing to sacrifice his own life to do so. He desperately wants to help others, to protect others, often to his own detriment. Despite the fact that, by the end of the series, he is well aware he was manipulated and brainwashed into becoming the Digimon Kaiser, he continues to hold himself accountable and carries the world on his shoulders.
Ken values intelligence and appreciates those conversations with Miyako and Koushirou, but he never judges anyone who doesn't have the same ideals and is happy to talk to others, especially Daisuke, about almost anything. He feels a strong sense of right and wrong, and he is more than willing to fight for the people and things he cares about. Because of the Dark Seed and his history with Darkness, he has a limited understanding of that power and is able to tap into it when necessary.
But despite their many differences, Ken and Daisuke are both determined and strong-willed, and above all else, they both have a big heart and love deeply.
From the very beginning, even while Ken is the Digimon Kaiser, Daisuke and Ken are linked, and that connection cannot be severed or broken apart.
As the Kaiser, Ken hyper-focuses on Daisuke in a way that has spawned many foe yay fics, especially the moments when he goes after him specifically — like when he chains Daisuke to a cliff wall for their first actual meeting. And when they meet officially as Ichijouji Ken and Motomiya Daisuke on that fateful soccer pitch, Daisuke has an insta-crush. He's thrilled when Ken remembers his name after the game, and that joy is crushed later that day when the Kaiser reveals himself to be none other than Ichijouji Ken.
But the moment Daisuke touches the Digimental of Miracles, he can feel Ken's kindness, his gentleness, and he knows that Ken is good.
When Ken shows up in the Digital World again and helps defeat their enemies, Daisuke invites him to join the team despite the rest of the group's hesitation and dismissal. Daisuke takes the train to Tamachi just to meet Ken after school and convince him to apologize and join them, and even though Ken isn't ready to join them and doesn't think he deserves their forgiveness, Daisuke has unwavering faith in him — and that is an essential part of Ken's character arc and healing process.
This is never more apparent than in the first Jogress evolution scene, where Daisuke literally slaps Ken to break him out of his desire to sacrifice himself for his crimes. The way they understand each other in this moment is profound, and it sparks their Digimon to evolve into Paildramon for the first time.
Jogress evolution, by its very nature, requires the human partners to understand each other on a deep, spiritual level, but no one — not even Taichi and Yamato — does so with as much depth as Daisuke and Ken in this moment. They literally hear each other's heartbeats, and they are the only pair to experience that. During this time, they work in perfect sync, even though they've yet to become proper friends, and later that night, they literally stay awake in bed thinking about each other.
But it doesn't take them long to bridge the gap and become best friends. Because if Daisuke understands Ken on a fundamental level, Ken understands Daisuke as well. He believes in him in a way no one else does — with plenty of reason to. He never considers Daisuke to be stupid or selfish or simple, and he has as much faith in his ability as a leader and a friend as Daisuke has in him.
When Ken struggles, Daisuke is the one who is able to get through to him, whether that is talking him down from what is essentially suicide or giving him strength to fight the darkness and open the Dark Gate. He also functions as Ken's knight in shining armor, as shown when Daisuke rushes to Tamachi to help Ken, since Ken and Wormmon are stuck there alone with the Dark Tower preventing Wormmon from evolving to Stingmon. This is most apparent, though, during the Demon arc, wherein Ken is kidnapped and Oikawa scans his neck to copy the Dark Seed, and Daisuke literally chases down the truck they're in on the back of Lighdramon.
And Ken helps Daisuke too, though not explicitly. At the beginning of the show, Daisuke has few real friends and doesn't seem to understand what friendship means, but as he and Ken become friends, he learns and mellows out. Plus, Ken's complete faith in him has to be good for the self-esteem.
When they fight against BelialVamdemon in the finale, we get to see how important Ken is to Daisuke. Throughout the show, Daisuke remains strong and confident despite rarely having the team back him up, but the moment Ken starts to break down, Daisuke practically begs him to stop because he won't be able to remain strong and defeat BelialVamdemon if Ken falls apart. Ken is his only weak spot.
There are a lot of explicit and implicit ways that Daisuke and Ken show how much they care about each other, and it's clear as the Adventure Verse progresses, most notably with Digimon Adventure: Last Evolution Kizuna, that they remain close. While Daisuke travels via Digital Gate to taste ramen from all over the world, Ken is the one person he regularly takes with him.
Daisuke is the most blatantly bisexual character in Digimon (though perhaps tied with Miyako), and while Ken's sexuality is far less obvious due to his subtle nature and the fact that they're literally 10-11 years old during 02, Ken's physical reactions to Daisuke — the blushing — imply plenty. Not to mention the way they look at each other, like they truly are each other's world. In fact, they're constantly looking at each other in all the promo art too.
A short note on their Christmas duet: Every Jogress pair sings a Christmas duet on the 02 Christmas Fantasy album, but unlike the other two pairs who sing classic Christmas carols, Daisuke and Ken's duet is one that was written specifically for them.
Also, this is a small note but even the official website lists the Digimental of Miracles as also belonging to Ken.
And as a final point, it's important to talk about Japanese honorifics, which demonstrate how close characters are. For instance, using someone's first name without an honorific signifies a deep, intimate relationship, though some younger people are less likely to use honorifics in general these days.
Daisuke, on the whole, is not big on honorifics and only uses them with the other characters sparingly. He only uses honorifics with Ken during their soccer match before he knows Ken is the Kaiser, and he drops them immediately afterward. Once Ken is good, he continues not to use honorifics, preferring to call him "Ichijouji" instead and, after a while, "Ken," though he switches back and forth between the two for the rest of the season depending on the circumstances.
Ken, however, is much more formal, and for the longest time, he refers to Daisuke as "Motomiya-kun." It takes him a while to drop the honorific, but he still refers to him by his family name. This is particularly interesting considering he refers to the rest of the 02 Chosen Children by their first names with formal honorifics for the entire series, even during Kizuna. This shows that Daisuke is a special case — by using his family name, he's being particularly respectful but the lack of honorific also implies an intimacy he's not emotionally prepared for. This makes the moment he calls Daisuke by his first name (no honorifics) incredibly meaningful. But it still takes him a while to adjust to using Daisuke's first name — it only happens once in the anime, though he becomes more comfortable and uses it regularly in Diablomon Strikes Back and Digimon Adventure: Last Evolution Kizuna.