Theories
There is at least one main theory revolving around a canon relationship (not essentially romantic, though) between Sesshoumaru and Kikyou. Said theory branches out into two sub-theories, leading to romantic involvement between the taiyoukai and the miko. What we’re going to do next is to demonstrate the main theory, taking our time to analyze the small facts we take as proof of the idea we’re standing up for, and then describe the following sub-theories, explaining how they could lead to a romance between the two characters.The starting off point here is that, somehow, Sesshoumaru and Kikyou know each other, not necessarily being ‘close friends’, let alone lovers; they have simply met and learned a little about each other. When or how that happened doesn’t really matter; one could’ve just run into the other in a forest, likely because of the chirpy Rin, and started out a ‘nice’ conversation, or in a heated battle between the proud taiyoukai and the rather stubborn miko, be it over fifty years ago or after Kikyou’s resurrection. The fact that should be kept in mind here is that one would have knowledge of the other’s existence, as well as who they are and what they want.
A few facts go against this theory. For instance, Sesshoumaru and Kikyou have little screen time, and they have barely met throughout the series, giving out little solid proof for any link between the two other than the “He/she-knows-she/he-exists” type. Also, in episode 116, Sesshoumaru looks at Kikyou and wonders if she is the same miko who sealed his brother to the Goshinboku, and if he really knew her, than he’d be sure she indeed was said miko.
Other details, however, point at a somewhat deeper connection between the two, and that same line of Sesshoumaru’s from episode 116, when he glances at her from the corner of his eyes and thinks: 'Is that the same miko who sealed Inuyasha...?', is a good example. So sure, we all know Sesshoumaru has, at least, HEARD about Kikyou, since Jaken kinda told him Inuyasha had fallen in love with a human miko and she pinned him to a tree... But the point is: there are quite a lot of mikos wandering in the Sengoku Jidai, and only one woman among them was the guardian of the Shikon no Tama. Sesshoumaru wouldn’t eye Kikyou and wonder if she was that special miko if he hadn’t at least an idea of what she looked like; he is just NOT the type of guy that would ask himself “Is that the miko?” each and every time he spotted a different priestess! That little quote might mean that he has not only heard, but seen the undead miko in the past, and is just unsure whether that woman who saved Rin was indeed Kikyou, after all, she –did- die 50 years ago.
In episode 124, when Inuyasha asks his brother about what happened to Kikyou, Sesshoumaru says something like "Kikyou was killed by Naraku." Notice the way he mentions her: he didn't call her "that woman" as he did before, nor did he refer to her as "that Kikyou person", keeping that touch of distance and indifference. He called her by her name only, and people usually don’t call others by their names unless they are close to or at least know them, right? However, the bigger hint is seen in the first movie. There's a scene in which Kikyou is standing near a cliff and, when Sesshoumaru approaches from behind, she SOMEHOW knows it's him without even looking back at him... And I'm pretty sure she knows he is related to Inuyasha, because, out of the blue, she says "I'm going to see Inuyasha." And then they talk a little bit more, and they sound so casual... Besides, that scene wasn't really needed in the movie, but it must have been there for a reason! They can’t have added that scene to the movie just for the fun of it, which leads me to think the reason why it was there was to show everybody that Sesshoumaru and Kikyou have met sometime in the past!
Now that those facts have all been cleared out, we move on to the sub-theories, derived from that main idea. The first one points at a meeting between the two fifty years in the past, when the bellflower was still alive. Out of curiosity solely, Sesshoumaru could’ve gone after the ever-so-famous Kikyou, the powerful miko whom all other demons talked about, and eventually fell in love with her, but either he never confessed to her for the sake of his pride, or Kikyou chose to go with Inuyasha, for the possibility of having a normal life beside a human man. (Being a hanyou, Inuyasha could use the jewel to become fully human, while Sesshoumaru could not.) That would explain his hate towards his younger brother and all humankind, as well as his somewhat indifferent attitude towards Kikyou whenever they meet. However, in spite of the resentment he felt for Kikyou for having left him in the past, his old feelings would still linger on in his heart, and the love she possibly would have had to lock away years ago could finally be revealed to the taiyoukai.
Another sub-theory is that Sesshoumaru and Kikyou have met randomly on their never-ending, aimless journeys and, somehow, came to know about each other’s similar goals (to destroy Naraku and bring Inuyasha down), thus forming some kind of secret alliance that would only be revealed, if necessary, during the final battle against the dreadful hanyou. Knowing that Naraku’s specialty is to manipulate people and have them do exactly what he wants them to do, the underground partnership between the two would come in handy, a trump-card of sorts, but in order for that alliance to remain a secret, they’d have to disguise it, to pretend they barely know each other so that Naraku would never suspect of any connection between his most feared enemy and the taiyoukai lord. But of course, during their furtive meetings, the bond between Sesshoumaru and Kikyou could grow deeper and go further than that of two mere acquaintances…
Anyway, should you be wondering where I got those theories from...I got them from my own, insane head! XD Yup, that's right, that's the outcome of a brilliant, yet slothful mind... Hee^^;