Now this kink goes way back to the late 60s when Star Trek fanzines started sprouting up. And it's still around in various iterations. From folks focusing purely on the visuals to writers to a combination.
K/S slash fiction was developed in mostly a vacuum. The writers (and illustrators) didn't have Buffy/Willow or even Sherlock Holmes/Watson fiction to refer to. Rather they just went for it. And if you watch TOS (The Original Series) closely, you'll see Kirk and Spock do have intimate moments of caring and passion (nonsexual) up for extremely liberal interpretation when you really want a certain type of connection to be there.
Though seeing kissing or penis mouth ass stuff is rather impossible so folks had to get creative. Never having actual gay characters on the show (until recent and upcoming reboots) also fed the need.
I'm a huge Star Trek fan and never actually got that vibe from the show much, but did find the two individually attractive. Though Spock rather sexually intimidating owing to the violent nature of plak tow and pon farr.
And Kirk generally too busy hooking up with space ladies.
But together you have the passion and the logic. It's flawless really. And K/S is not the only Star Trek slash out there. There's a lot of Sulu/Chekhov. And stories with Uhura, Bones, Scottie and Next Generation characters. Then there are the most perverted, bizarre of all. Totally nonsexual stories that just are in the Star Trek universe, explaining what happened in the timeline during a random shuttle trip or what happened on a planet after the Enterprise left.
Ultimately, slash fiction and images say more about the creator than the original. Meaning, I want to meet the creators and slash fiction our bodies together into an ecstasy of phaser bursts and mind melds.
Or something like that.
So just Google the hell out of this if you want. Rather hit or miss but you'll find it.