I'm afraid I can't help on African breads but here's at least a few leads.
I have seen Afghan bread (or bread labelled that) both at People''s Market in Evanston, and stacked up near the register at the otherwise generic corner store on Bryn Mawr directly across from that Mia Francesca location.
Middle East Bakery off Clark in Andersonville has not only pita, but long sesame seeded flat loaves, some that are crepe-thin (whose name I forget) and a couple of other varieties.
I believe that the Mexican bakery just south of the Irving Park red line does a good job, but haven't been in in a while, and of course, there are many panaderias to choose from.
At least one of the places that produces tortilla chips, tortilla's etc. locally for retail sale offers tours. I forget which brand it is, possibly El Milagro, but I'm not sure. You could check that out and it might be a real blast for the kids.
And of course there's Limpa and other Scand. breads i Andersonville and all the Indian and Pakistani breads you could find along Devon.
Perhaps if you went into any of the African restaurants along Broadway toward Devon you could get some info on finding African breads as well.
Just a few ideas. Others may have better, more complete info to offer.
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