Is it possible to bake bread or the like using a stovetop tagine?
I've cooked bread on the stove many times. My setup was a cast iron pan with a metal trivet inside and a small pot inside that, which is what the bread dough was placed in. I then had an old rice cooker pot inverted over the pan. That essentially created a small stovetop oven. The small pot was on the trivet so the pot didn't get direct heat from the cast iron pan - otherwise, the bread would burn on the bottom. I did this for many years to make one or two servings of bread every morning for breakfast. 

You could likely do something similar in your tagine. Figuring out the timing for the bread was trial and error. There's just no other effective way.

As for flat breads, I cook them using my cast iron or carbon steel frying pan. I've tried baking naan, but we don't like the texture of it, so frying is the way to go for us.