I’m really surprised no one asked after my little discussion of HP and Houses and all that. And of course you give me the hardest one to contemplate.
So this is all subjective (obvs) and based off my own interpretation, but really I think a lot of it comes down to what his biggest driving force is and who he is as a person under everything he piles on himself. (And I’m not doing that whole Kylo is X but Ben is Y because they’re the same person.)
Kylo Ben is clever and curious. He’s kind of quiet (outbursts aside, he doesn’t actually talk that much). He’s emotional. He’s also impulsive. He’s a bit of a traditionalist (don’t remember where but I’ve heard the argument that part of the tension between him and Hux is traditionalist vs technocrat and I can see that). It’s be speculated that he’s creative (calligraphy set). And he’s an idealist (the whole “I want to remake the world as I think it should be” thing). And, lest we think I’m only talking about good qualities, he’s also a snob and an elitist.
I don’t see him as a character willing to do absolutely anything to achieve his ends. To me, he doesn’t read as particularly malicious. Desperate and reactive, yes, but not malicious. A good 80% of what he does seems to be a result of trying to get the confusion and pain to stop.
All this to say I’m torn between Ravenclaw and Gryffindor. There’s no way I’d put him in Slytherin. Slytherin gets a bad rep for being malicious and deceitful, but the traits I more associate with it are ambition, cunning, and willingness to do whatever needs be done to get what you want. While he is clever and cunning, I don’t think he’s that ambitious. His main character conflict isn’t “I want power and people are stopping me” it’s “I want to not be conflicted but this stupid conscience is getting in the way”. I also think he’s more desperate than he is actually willing to do underhanded and potentially deceitful things to get what he wants. He’s not a liar. He might omit the truth to Snoke, but he doesn’t lie. He’s much more earnest than that. (If he were willing to do and say anything, he would’ve lied about Rey’s parentage. He would’ve used the fact that she wants a family more than anything against her and either told her he was related to her or that he could help her find her family.) He’s not a Hufflepuff because he’s not a good “finder” nor is he very patient. His Gryffindor traits are more to the forefront (that reckless, impulsive, proud, “I’ll give ‘em Hell” attitude he gets from both his mom and his dad) and his Ravenclaw traits are more subtextual (asking questions, trying to figure things out, thinking, all the certified nerd stuff) so it’s hard to say.
I personally would probably put him in Ravenclaw, but a solid argument could also be made for Gryffindor.