I'm told you'd probably need to go to Jerez to see an authentic Flamenco session nowadays, (at least of the cante jondo type, the deepest form) - they barely exist even in Sevilla. Most of the shows everywhere else are for tourists.
The saeta that they sing in the semana santa processions is a form of flamenco is quite something if you get the chance to witness one being sung.
Not that I'm an expert or anything, there are so many different styles of flamenco, it's incredibly complicated, I don't pretend to understand it.