Flamenco show - Madrid

Check out Yolanda (Yoly) Martin's blog: https://theflamencoguide.com/flamenco-blog/. She is fantastic. We took a private tour with her in March 2020 (we were her last tour before everything shut down). We went to Las Carboneras.
She's on maternity leave and there's no indication of when she will return to giving tours, but I highly recommend her. She is the wife of James Blick, cofounder of Devour Tours, who also has a YouTube channel called Spain Revealed.

Are there any flamenco shows that’s not in the highly touristy areas? I’m curious. Maybe the OP might find the answer helpful, too.

Okay, I never like questions that ask "what is the best?"
All opinions are subjective, and even more so with art.
Flamenco is a magnificent form of dance art, and can be very personal.

Do you know anything about flamenco at all, and why some dancers are highly recognized? I took flamenco lessons for multiple years, and the hardest thing I ever experienced was trying to learn off-beat movement from an expert.

For me, all flamenco shows are discoveries, and all dancers are creating and sharing their individual styles. I would attend a few different shows, just to get the flavor of the diverse dancers, or the focus of that particular troupe. Some places may be more traditional--others may incorporate more modern trends.

Some shows offer full meals--others just provide snacks. Do you want to go to a theater you can walk to from your hotel, or go with a group?

I am sure whatever you choose will be an enjoyable and lovely experience.

BBC's "The Arts Hour" latest show featured an all female flamenco group, Las Migas, "On tour in Madrid." (starts at about 27 minutes in). Las Migas won the 2022 Latin Grammy Award for "Best Flamenco Album." You might get lucky and catch them in Madrid.
https://www.youtube.com/watch?v=ISdmL28DkO4

To me, the best flamenco is that which is performed at fairs and festivals, not at the tourist oriented venues. Not that those shows are bad, but not my preference. Watch a couple videos to ensure you really want to spend an hour or so listening to it. A little flamenco goes a long way.