is dave crushing on karkat??
...-shrug-
I honestly don't know. I never settled that question in my head before deciding to write him, as it felt too fun keeping it ambiguous. I typically lean towards "Yes, absolutely," both because that pleases my multi-shipping heart and because it could make for good drama, but it could also very well be Dave just being Dave. He's a flirty shit, can sometimes suck really hard at reading the room (a symptom of his autism), and has an almost zen-like ability to outwardly not give a shit what anyone else thinks about him, even when he absolutely does care all of the time. So all the flirting could just be him amusing himself. Karkat and Kanaya both seem to think there's something to it, but they're as unsure as I am since he's so hard to nail down.
If you're looking for a definitive answer, the best I can do is to say that he's known Karkat for a long while now and hasn't actively confronted him with a love confession, but if Karkat for some reason approached him one day and was like, "Hey, want to shove your tongue down my throat and grab my ass?" he'd pretty readily agree.