Moving forward in time the ottomans and mamluks had symbols on their flags (I don't know how to hyperlink on mobile but they're easily wikiable) so I wonder if maybe a pertinent follow-up question here is at what point did the states in this region start putting symbols on their flags and why?

It's not so much that they had simple flags as that the Europeans had remarkably complex ones. The European emphasis on landed nobility with hereditary titles differs sharply from the iqta system employed by the Islamic states.