I'll tweak this recommendation and say that I'd probably not ask outright "how'd it go" to the final interviewer (they may not really know at this point anyway). Instead, I might look to say something to the effect of:

"I'm always looking for ways to improve, and I've found in my career that interviews are a great way to expose oneself to new growth opportunities. If you, or anyone on the team, has some feedback based on the interview, regardless of whether or not I get the position, I'd love to hear it."

This has the added benefit of showing a few things:

[1] You're committed to growing and improving. [2] You're open to feedback. [3] You're showing you'd value their team's opinion, which signals your own interest in the team.

Mind you, a lot of companies won't want to share any information for legal reasons. Not much you can do about that, but it never hurts to ask.