"with which platform" vs. "on which platform"

A "platform" is literally something one stands on. In this context, we still use "on" to describe the content on a streaming platform. But even leaving this very recent terminology aside, idiomatically, we have always said that we watch things "on television", not "with" television.

If you are looking for something more natural, I would say that the word "platform" is not used that much in casual contexts. Though widely understood, it is still really technical terminology.

I think the most natural responses would probably be "what shall we watch it on?", or simply "what on?". You could also ask "on Netflix?" which would elicit either a confirmation or a different answer.