Flamenco AND Bullfights are best found in Madrid of the two cities you're considering. In fact, I don't think you'll find a bullfight IN Barcelona city anymore anyway - you'll have to go to a village somewhere outside the city for this. I'm certain there is/was some discussion on where/how to find bullfights near Barcelona here in this category. Try a SEARCH to find it using keywords
BULLFIGHT BARCELONA.
You will find Flamenco in BCN for sure but that's kind of like watching Flamenco in Paris, if you ask me - it just seems so "out of place" and unnatural. Flamenco and bullfighting (to some extent) is more indigenous to the central and southern regions of Spain.
Madrid really does have it all for these two "spectacles" - and there are many choices of Flamenco dinner shows. Be forewarned that "flamenco food" has a reputation of not being of the highest quality. That is to say, it's fine, it's edible, just nowhere near as good as you'll find at a normal restaurant. You'll also find a number (MANY!) of threads on Flamenco in Madrid by conducting a search. I've only been to one (
Café de Chinitas ) so I can't be objective not being able to compare it to others. It was fine, entertaining, but we didn't have dinner there only the complimenarty pitcher of sangria and a tapa of olives, I think.
Best of luck and enjoy your time in Spain!
Saludos, MadridMan
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