You need to understand that flamenco rhythm is very different from classical or popular music (it has more in common with Indian Classical music and the concept of "Tala").
All flamencos talk about rhythm using the notion of "compas" - these are rhythmic "styles", that include a time structure, as well as a feel and a usual tempo. For example, Bulerias compas is a cycle of 12 beats, but sometimes just 6, played fast (and faster!), and has a feeling of "fiesta", both dark and light, about it. So when one of your answers refers to a Paco de Lucia song as "Bulerias", he is mistaking the name of the compas for a song title. And Paco is certainly not playing in 3/4 - the "uncommon" time signature you are hearing is coming from taking 12 fast beats and grouping them by threes and twos (Google "hemiola"), and with Bulerias in particular, often throwing in an accent on beats 7 and 8 (with 12 being the first strong beat of the cycle).
"12 being the first strong beat"?!? Another amazingly confusing thing about flamenco rhythm is that traditionally flamencos count the 12 beat cycles (Bulerias, Solea, Alegrias, etc.) starting with 12, instead of 1. This seems just perverse, until someone reminds you that they refer to the "clock" - and the clock starts ticking at 12...
OK, ok, there are simpler compas - "Tango" is four 4/4 measures (but the cycle usually ends on beat 3... And it doesn't really have anything to do with Argentine tango...). Obviously, people can go on and on about this topic - it's a great stew of old dance forms (think Sarabande, from Bach's time?), ethnic music (Zambra, from the Jews of Cordoba), modern "whacked" rhythms (they rap to flamenco in Jerez) and ancient mystery (compas really are like Indian Talas).
But since you are just looking for flamenco "spirit", and aren't necessarily committed to Total Immersion Flamenco Obsession, I would first just focus on trying to hear those squirrely groups of twos and threes, and how they shift throughout the 12-beat cycle. But if you get curious, there's lots of material on the web (a good start is the Wikipedia article on flamenco - and then just start typing the names of various compas into YouTube). Have fun!