Kathak is the precursor to flamenco.
To be more specific, kathak as it was practiced in the 11th century (when the gypsies are thought to have gone to Spain and created flamenco along the way by grafting other cultural influences) is the precursor to flamenco.
If followed the trail of those gypsies, would we be able to pinpoint the changes in kathak and understand the methodology of changes in tradition better? Would we find specific ruptures or generation to generation fluidity within the modifications? Was it one band of gypsies that popularized it or several who made similar changes across space? Why and how did the guitar come into play? The shoes? The change in costume?
To that end, what of the Mughal era in India where kathak as we note it now came into existence? I wonder if kathak had the same rupture from its past as bharatanatyam did during the British takeover, from changing the form quite significantly to even changing the name...
It would be extremely interesting if someone did a comparative study of the Mughal and British eras to see how these two cultural takeovers affected the art around them. I'm sure you would find some sort of patterning or similarity in the way kathak and bharatanatyam was created. Of course, there are the obvious ways where the government sponsors political art that lauds their system, and art that comes out as a means of protest (Hedayat's book The Blind Owl or much of Picasso's work). But can we expect that the oppressed in the Mughal era were just as conscious of the change and similarly protested against the changes in the traditional aspects of their form each time? In short, did kathak artists also do their best to resist change and as a result stagnate and codify their form for a bit?
Or perhaps, as is my usual M.O., I am overestimating the significance of the changes that occurred.