Flamenco isn't originally a Madrid tradition — it developed in Andalusia, in southern Spain — but the capital has one of the country's strongest scenes for seeing it performed well today.
Flamenco emerged among the Roma (Gitano) communities of Andalusia, blending Romani, Moorish, Jewish and Andalusian folk traditions over centuries. It's built on three elements: cante (singing, arguably the emotional core of the art form), toque (guitar), and baile (dance) — the dancing that most visitors associate with flamenco is actually the newest of the three to develop.
A tablao is a dedicated flamenco venue, distinct from a restaurant with dancers as background entertainment. Signs of a serious one: a small, focused room built around the performance rather than a big dinner theatre; performers who are working musicians and dancers, not a rotating tourist-season cast; and a program that varies rather than a fixed, identical show every night.
A proper show runs 60–90 minutes, often with dinner as an optional add-on rather than the main event — going for the show with just a drink is completely normal and arguably lets you focus better. Expect intensity rather than polish for its own sake; flamenco at its best is raw, not glossy.
Good tablaos in Madrid do sell out, especially Friday and Saturday nights — book a few days ahead rather than trying to walk in.