Wow, that's amazing! I was 19 when Paco passed away, and I didn't even discover flamenco until a few years ago. I can't imagine how amazing it would have been to see him play live. Of course with youtube today we can view many videos of him playing, but this is hardly a good approximation of a live performance.
A note on the origin of flamenco (disclaimer: I'm definitely NOT a flamencologist, so get a good amount of salt before reading this):
There is some consensus that the Romani people originated from the northern Indian subcontinent, migrated out of India (~500-1000AD) westward, and eventually made their way via the middle-east and north Africa to Europe and subsequently many other parts of the world where they now live in diaspora populations, including southern Spain. I am tempted to think that the artistic and cultural heritage of the Romani people as regards flamenco has many roots in the artistic and cultural practices (song and dance) of certain groups from India -- for instance we can draw many parallels between the Kathak dance and Flamenco baile, but this might be based more in pareidolia than historical fact (although the similarities can be glaring). Moreover, the migration of these peoples out of India entails several centuries of migration in which culture was influenced by comingling with other groups and peoples in different places at different times. Some trace the earliest arrival of Roma in Spain to the 15th century, coinciding with the end of Moorish rule in Spain and the beginning of the inquisition. The inquisition entailed persecution of certain groups, including the Moors, Jews, and Gitanos, and it has been suggested that the basis of flamenco started to form with the persecution of these groups -- hence the purported Moorish and Jewish influence on the music (especially in the cante). The development of the music from here to the 20th century also entails some integration of western European music (like the introduction of the fretted, equally tempered guitar and some classical harmonic norms).
This is all to say that it is entirely possible (and perhaps highly probable) that for a very long time, song and dance has been in the blood and culture of all those generations who came before the gypsies in Andalusia. The origin, history, and development of Flamenco before the late 18th century is extremely complex, enigmatic and inescapably mysterious; thus in my opinion it is not useful to consider Flamenco as an approximation of Arabic music nor any other style of music as it's origin entails a myriad number of cultural influences. Rather, we should consider Flamenco as a thing-in-itself, born in the hearts and souls of the gypsies of Andalusia, whose heritage belongs not only to those persecuted and oppressed peoples of Andalusia and Spain but also to the entire history of the world and of human endeavour and passion. Perhaps we should consider all music this way.
Concerning the "music theory" of Flamenco: if we think of music theory not as a set of fundamental rules that we must employ and never break in order for our music to sound good, but rather as a set of conventions and traditions that have been developed and handed down within a genre or sub-genre of music that are themselves subject to breaking and experimentation, then we may perfectly well formulate a music theory for flamenco by observing and aggregating what flamencos do and have done by identifying common melodies, chord shapes, progressions, runs, etc. Perhaps you are looking for a complete systemization of flamenco music -- but the music and tradition is typically somewhat averse to this. For instance, a major difference is that in jazz (I'm not knowledgeable on this honestly) there is a big focus on things like modulation and re-harmonization as well as particular attention on functional harmony and chord extensions on top of the basic seventh chords, and these things just aren't too important in flamenco because for the most part we are just in phrygian, sometimes major/minor, and really the only explicit modulating we do is between these 3 modes. But I'm hardly an expert when it comes to music theory so... if you would like to dismiss my thoughts on the matter, you might be right to do so.
Okay one last thing lol (I definitely like to ramble, sorry): concerning arabic scales, the only intervals in arabic scales that are tuned using just intonation are the octave and the 5th (using the third harmonic). The oud for example, it's strings are tuned in 5ths (or 4ths depending on how you "look" at it). The oud is fretless. On any fretless stringed instrument, theoretically speaking, there are infinitely many tones that may be produced on any one string (a.k.a. course) of the instrument (there are infinitely many points at which we can place our finger on the string, hence there are infinitely many different tensions we can hold the string at, hence infinitely many distinct fundamental frequencies the strings can vibrate at, assuming the length of the neck spans a single octave); realistically, due to the limitations of our ears and the size of our finger tips, the number of tones we can play/distinguish are finite, and the best among us could probably differentiate something like 50 different tones on a single string (that's a complete guess btw). Beyond the octave and the 5th, some notes fall on familiar tones of 12 tone equal temperament (12-TET), and some are microtonal deviations away from 12-TET.
Googling it now, I see that there is in fact a 24-TET system that is used to notate different kinds of arabic music -- yes it is equally tempered, and includes all the tones of our 12-TET as well each tone half-way in-between the consecutive notes of 12-TET. Wikipedia says that there are in fact scales and modes (called maqamat) in arabic music and that there are over 70 of them. I assume that, like traditional indian music which also utilizes microtones and similar vocal devices (like ululating), there is a rich history of music theory and tradition in different arabic and south-asian cultures. So there are indeed systems and standards of music theory in arabic music, although it seems quite unlike the western tradition in many ways.
In any case, as modern westerners, it is highly tempting to fit all contemporary music into the framework and paradigm of western music theory. But it can be a humbling experience to realize that, for thousands of years before the advent of, say, monophonic ecclesiastical plain chant (as an arbitrary marker of the beginning of the western music tradition), humans were practicing music completely detached from this paradigm. We modern humans are completely spoiled, from the get-go, with the wealth of musical history that has preceded us. I mean how many years of primitive experimentation and development of musical ideas and instruments did it take to get us to this point? It is a tragedy how much remains -- and will remain -- lost forever to time. Sorry for rambling so long, but sometimes I just can't help it.