Millie and Kate

Actually yes, I got the same feeling while watching the movie. I found this interesting read:

When Kate leads Densher up the stairs(as she had led him up the stairs in the Underground) to the billiard room when he arrives at one of Aunt Maud’s parties on the arm of another woman. [...] Though Kate testifies to the emotional pain she has suffered as a result of her separation from Densher, her words suggest as well her perverse pleasure in that pain, for immediately after kissing Densher, Kate commands him to return to his date and “kiss her with that mouth.” The decadence Rowe refers to attaches itself here most securely to Kate, who is obviously aroused by her embrace of Densher in her aunt’s very house, by the power she wields over Densher, and by the thought of indirect sexual contact with another woman through Densher’s body.
Ruth Bernard Yeazell writes about the film’s success in rendering what she
calls “the novel’s dream of triangular intimacy” through its visual emphasis on
Kate and Milly’s attraction to each other, and in its depiction of Kate and Milly looking at a pornographic illustration of three−way sex (90−91). Her point is that critics who fault the film for its “vulgar eroticizing” of the connection between Kateand Milly overlook the strength of that mutual attraction as represented in the text itself (90). But while Milly and Kate are genuinely drawn to each other in James’s novel, which makes it possible for readers to believe that love for Milly at least partially informs Kate’s actions, in Softley’s film the possibility of lesbianism becomes associated with Kate’s general sexual decadence and taste for the outré, including, perhaps, troilism.3 Kate becomes sexually opportunistic as well as financially avaricious, not above cultivating a flirtatious intimacy with Milly in order to steer her into Densher’s arms, and her money into Densher’s pockets.

3 Diane Sadoff remarks of the film that “Indeed, the sex in Wings always suggests a three−some” (272).

http://www.asc.uw.edu.pl/theamericanist/vol/22/22_131-142.pdf

I admit I did think they were going to engage in a threesome at some point. Kate seemed more than a little infatuated with Millie upon first meeting her. It's telling that in the scene in which Merton and Millie were dancing, Kate was mainly focused on Millie; it is unclear who she was jealous of in that moment.