How to cook flatbread without oil?

My family always made these Chinese flatbread-like pancakes and we cooked them on a cast-iron pan (although it was more like a frying surface or something, it was flat, round, had a handle, but no conceivable border) without using any oil. Now it is true that a little bit of the flour kept sticking to the pan, but we also had a little broom made of spliced bamboo (I think) with which we just swept the excess flour off. This of course is rather messy, but we only had to clean the stove after the cooking was done. I think this worked so well because the dough was not too wet (but also not too dry) and we covered the surface of every flatbread with a little bit of flour, which helps in making it less sticky.

A wide enamelled dish on top of the stove might work nicely. I've got a le Creuset that I use for all sorts of things, but my excuse for buying it was flatbreads, which it does very nicely. They don't stick at all unless they're much too wet, and any split flour can just be dusted out between breads. As it's cast iron it also has a nice even heat, which reduces burning.

When you tried baking them, did you use a baking stone? How did you bake them, exactly (i.e. time and temperature used, did you preheat, etc.)?

I suspect using a baking stone with sufficient preheating ought to give you the texture you are looking for.

Have you tried putting them in the microwave to heat through and then just putting them either in a bread toaster or toaster oven for that crispness? Or placing the bread on aluminium foil to protect the pan or in a toaster oven?

I make flatbreads on a really hot cast iron griddle -- but I don't cook them all the way through if I'm cooking for multiple people. I cook them until they're charred enough to release, and then I move them to a moderate oven to finish cooking through. This might allow you to speed up your cooking and minimize burning.

If you do need to clean the pan between batches, I'd recommend finding a stiff-bristled brush that can handle high heat. I have one that has wooden bristles that's just labeled 'pot brush'. It allows me to quickly knock off any loose debris that doesn't require much scrubbing without needing to wet down the griddle. I've also been known to take a metal spatula to scrape down the surface if needed. (I've filed down the corners of my spatulas to reduce the chance of gouging the surface).

Another option would be to cook the flatbreads on a grill. (a real grill, just just a grill pan). Any loose flour would just fall into the flames below.

A change in technique might help, at least to keep the dough from sticking. As for random dustings of burnt flour, they can probably be brushed out dry or just left till the cooking's over - even burnt it isn't harmful. Disclaimer, I'm more familiar with chapatis or tortillas, so there might be some other differences with your specific flatbread and its dough, but the basic technique is pretty helpful.

I've found, when making chapatis or tortillas, it helps if the surface is quite dry (like dusted with flour, and brushed off). It helps a lot to hold one side of the dough, and sort of slowly sweep the other half over the hot pan, then do the other half (of the same side) before settling the dough on the pan, that side down, spend a second or so moving it around in the pan, skittering it with my fingers, to make sure it won't stick before leaving it to cook.

What exactly these few seconds do I'm not quite sure, perhaps warm or dry the surface a bit better or form the lightest crust, but it does seem to keep the dough resting lightly on the surface... and if it doesn't stick in the first few seconds, it isn't likely to stick at all.

As I said, if any flour dusts off it can be swept off with a brush, paper towel, etc, or else it can just be left till you're done and cleaned then. It won't encourage sticking, well not any more than the pan's actual surface will, if it won't come off brushing it isn't likely to come off on your flatbread, and it isn't harmful in such small amounts.

We made Dutch boys this weekend. It's a sort of baked pancake (quick bread) that includes no oil in the recipe, but it does rely on a heavily buttered cast iron pan, so not sure this is the answer you were looking for, but thought I would offer it.

Search for Dutch baby pancakes on the Google.