I'm not sure about this ship, I mean in some ways I feel like they really only spend time with each other because most people find Sparrow too annoying to spend much time with and it seems as though no one likes Duchess because of her nasty, scheming, selfish attitude.
Sparrow often seems, to me, like he is Duchess's side kick because he goes along with her plans to cheat someone else out of their destiny, such as when she tried to expose Hunter and Ashlynn's secret relationship. However, we do see him get sick of the isolation that he has to endure because he's known to hang out with her, in the True Hearts Day episode he complains that no one will tell him where the dance because he's friends with her. Then when Duchess's plans to tell Headmaster Grim about where the party is fails, he tells her that she got what she deserved.
That being said Sparrow does have a rather large ego, as he's shown on numerous occasions, one in particular being when he gives Raven a hard time about practicing for the talent show because "practice is for losers." So I'm not saying that he's exactly a saint either. Maybe that's why he spends so much time with Duchess.
Thus, I don't see a lot of chemistry between them, but I suppose I can understand why people ship them since they do spend a lot of time together, and to be honest I can't really see them being pared with anyone else.
I don't know why people ship him with Poppy O'Hair because, as far as I am aware, we never actually see the two of them together. I don't think that Poppy is the type to put up with his egotistical personality or his impromptu guitar playing, but I could be wrong. Maybe the two of them could work. Or I could ship Sparrow with Melody Piper, since they both have such a passion for music, they could bond over that, but I don't know.
So I suppose I do ship Sparrow and Duchess mostly because I don't see anyone else that I immediately ship either one of them with.