I don't think Kennit necessarily cared about Wintrow because he was Wintrow to start with - I got quite caught up in the idea of him using Wintrow as his stand-in for himself as a child after Vivacia makes them realise they're not so different. I think he recognises the abusive treatment Wintrow receives from Kyle, and then tries to make "himself" better. Of course, I don't think Kyle was anywhere near on par with Igrot in terms of how he treated Wintrow, but I think Kennit definitely picked up on how it was a similar thing. I originally figured that some of the things Kennit did, such as removing Kyle from the equation, were sort of done subconsciously to protect "himself" i.e., Wintrow. On a similar note, it also struck me where he decided to stash Kyle - he mentioned that the big house on Key Island hadn't been lived in since Igrot burned the town, and I thought maybe he was thinking that the "abusive father figure" belonged hidden in the house with all the other bad memories that nobody talks about.

I did start buying into the pair of them later on, though. At least, I think Kennit cared about Wintrow as much as he was capable of caring about anybody. If I think of the list of people Kennit was nice to for no other reason than because he wanted to be, I come up with Wintrow and his mother. With everybody else - Etta, Sorcor, even Vivacia, Kennit had an ulterior motive for being a sweetheart, and it was always me, me, me. Kennit is my favourite character of all time, but even I wonder at how they weren't suspicious of him sometimes, being such a jerk one second and the nicest person alive the next.
I also think it's possible that affection for Wintrow was actually imprinted accidentally on Kennit by Vivacia when they were all trying to put him back together again after he "died". Vivacia was one of the few creatures Kennit trusted and they did bond - I think Kennit may have picked up on her feelings about Wintrow, gotten completely confused, and then just decided to go with it because he trusts her judgement.

I know Kennit did tend to swerve towards thinking about doing to Wintrow as he was done by or even killing the boy off, but if I'm honest that didn't really surprise me. Kennit was brought up in a relationship which was characterised by violence and aggression, and learned very young that the best way of making sure all his secrets stayed buried was to kill the people who knew about them - wasn't there a part, possibly in Mad Ship, where Wintrow actually sees what happened to Kennit inside Kennit's own head? If I were Kennit, I'd be pretty eager to make sure that secret stayed secret, too.

(While I'm thinking about it, it could even have been possible that he wanted to get rid of Wintrow because he didn't want to get hurt. Most of us feel that way sometimes, but we were brought up in civilised environments and we know how to deal with it, how to keep people at arm's length without harming anyone, or even how to talk through those issues. Kennit wasn't brought up like that. I think Kennit probably cared about Igrot in the beginning - one of the ways I imagine Igrot getting in with Kennit's family is being nice to his "business partner"s son. But then Igrot hurt him, so Kennit finished him off, and the pain stopped. He would have learned that people are only nice to you for so long before they start hurting you. It's weird and I'm functioning on coffee so maybe it doesn't seem that , but I can sort of see how to someone as damaged as Kennit, that would make sense as a method of self-protection.)

I also recall Paragon remembering Igrot yelling at Kennit, saying something along the lines of, "Twelve years old, and if you don't learn to behave like a man on this voyage you'll never be one, you worthless pup." If Kennit was around twelve when he was with Igrot, he would have been starting to grow up, hit puberty, etc, so I'm also guessing he would have found it difficult to understand whether they were meant to be "father-son", or "together", which I thought he was also feeling later on about Wintrow. So while it did disgust me that he thought that way about Wintrow, I could sort of understand why he would think that maybe that was the way it should be between them, because that's how Kennit sees relationships - one person being dominant over the other. For him to feel safe, everyone has got to be either plotting against him - and therefore disposable - or submissive to him.

On a similar note, and now working completely on speculation: these days, people like Igrot often tell the child they are abusing that they're doing it because "You're special" or "It makes me love you." So if Igrot did that to Kennit, that would have warped Kennit's perception of how he can make people care about him. Also, it would further explain although not excuse why Kennit thinks sleeping with Wintrow is the way to go.

However, I freely admit I can be a little bit biased in defence of Kennit. I spent most of my first read of LST not understanding him, picked up on all the little hints about Igrot the second time around and then spent every read since trying to excuse his behaviour with the kind of ideas I put in this post, even though I don't condone it. I guess we all have that one favourite character that we're just a little bit silly about...mine's Kennit.