I know it was hinted in the game that Sialeeds found Kyle rather annoying and Kyle was just his usual pervy self with her the same way he is with everyone, but did anyone else get the impression that there was something more serious going on between them? What about the scene where Kyle barges into her room and says in this wistful way, "It's exactly the way she left it..." or he talks to the prince about her reasons for what she did. I heard somewhere that someone played a scene in the game whereby Kyle had intended to ask Sialeeds to marry him, but I can't find any information on this anywhere else?

I'm pretty sure Kyle had a thing for Sialeeds. He even has an extra special line for her if you add him to the party while she's already in it. I don't get the impression she returned his feelings, though.

Nah. She was special to him, in that she was a member of the family that he was dedicated to, so for that reason he would likely favour her above most other women in the army whom he had only just met, but I don't think there was anything more serious going on between them beyond that.