“Burka” as a term refers to one very specific style of veil (as a category all such types of coverings can be called “veils” or “hijab”, although “hijab” can also refer specifically to a simpler headscarf) which the entire face and body are covered and loose fitting cloth with the eyes covered by a screen that is semi-transparent from the perspective of the wearer.

Burkas are most closely associated with Afghanistan, where they were made mandatory by the Taliban, and with the tribal areas of western Pakistan, which have strong cultural and often tribal/familial connections across the Afghan border, particularly among the Pashtun.

Burkas were developed in this region of southwest Asia to satisfy not only Islamic strictures for women’s modesty, but also to satisfy the demands of “purdah”, which is a cultural practice of separation in South Asia, as well as the Pashtunwali honor codes of the Pashtun.

As /u/silverappleyard helpfully linked to in my previous post, belly dancing comes out of European interpretations of traditional Egyptian dancing. However, what the Europeans got was traditional dance as performed by prostitutes, rather than the pious dance troupes that performed the actual traditional Egyptian dances during festivals.

In Egypt, as throughout the Arab world, the burka is very uncommon. The most common historical style of veil until the 20th century in Egypt was the niqab, in which the body, head and face were covered, but the eyes remain exposed. You can see a historical example of that kind of veil here, from women protesting in the 1919 Egyptian revolution: http://3.bp.blogspot.com/_U_vpP7GD43k/TUTGHrQ2b6I/AAAAAAAAA_k/wVdr_lVUwu0/s1600/6a00d8341c630a53ef00e551813fe88834-800wi.jpg

In Egypt, this kind of ceiling was not, historically, strictly a religious practice, as Coptic Christian and Jewish women also wore this same style of veil.

As I relate in my post, the origins of belly dancing as we stereotypically know it are effectively a 19th and 20th century phenomenon. (The more general origins of scantily clad women dancing for money I imagine are so closely linked to human kind’s oldest profession that I imagine it might be a better question for /r/askanthropology.)

Veiling, by contrast is an ancient practice. High status women in the ancient and late antique Greek speaking world were veiled, a practice also practiced by ancient and late antique Persians. Although there are religious requirements within Islam that point to the veiling and separation of women or their need to maintain “modesty”, the most widely accepted theory about the development of Islamic veiling as actually practiced is that it was adopted by Muslims after the Islamic conquests in emulation of the practices of the newly-conquered Greek-speaking population.

To go back to your original question: I’m unfortunately not familiar enough with the dancing traditions of AfPak to know if any elements of similarity exist to belly dancing, but I haven’t heard of them.

I hope this is helpful, I’m unfortunately typing from a train, but the Encyclopaedia of Islam entry on “Hidjab” might be helpful further reading.

You might be interested in this fascinating write up from u/CptBuck on the origins of belly dancing.