Most of the recommendations I´ve seen here are for touristy "Flamingo shows" (exactly!) However, Madrid has the best Flamenco scene outside of Andalucia as many performers, for example from my hometown of Jerez, go to Madrid on a regular basis to work. If you can navigate through the Spanish, try
www.tristeyazul.com, get to the main page, and click on the link "Cartelera". There are quite a good number of good venues, such as the peña flamenca "El Duende" or Sala El Juglar in Lavapies. Not all of it is going to be flamenco dance, but it will be "auntentico"!