Following up in another way, Eskimo culture can be safely assumed to lack flatbread since the diet lacked pretty much any plant-based element. Any other non-agricultural cultures, like pygmies, would also lack the ability to produce bread. (Not to say they don't eat it today; pygmies are commercially entwined with the settled people around them.)

The obvious places to look are Polynesia (as mentioned), Australia, and sub-Saharan Africa. What are the indigenous flatbreads?