Although Duchess eventually develops feelings for Thomas, she is really his love interest, while Thomas has a crush on Duchess, right when he first meets her.
Thomas, at first, was obviously a little turned off by the fact that Duchess had three kittens, but he quickly took a liking to kittens became a fatherly figure to them (the real father of the kittens was never seen or mentioned in the movie, so it can assumed that Duchess was most likely a widow). Thomas helps them find their way back to their home in Paris, after their butler, Edgar, left them stranded. Thomas even risks his life for them, when he saves them when Edgar recatches them, to take ship them off to Timbuktu. In the end, Duchess and Thomas presumably get married, after he moves in with her family.
In the film, her speaking is provided by the late Eva Gabor while the late Robie Lester did her singing voice. The latter two even did the speaking and singing to Miss Bianca from The Rescuers.