Adding rolled-in seasonings to pita bread
I think the issue is that flatbreads are a single layer whereas pita and similar pan breads (there is an Indian version as well [paratha]) develop a pocket in between the layers (usually due to trapped steam).

For pan breads, I've noticed the amount of heat is very important.  Too much and it burns and too little and you don't get the pocket/lift.

In this case, the added wet ingredients might be preventing the steam from building up and forming a pocket.  Either by absorbing the pan heat in the area or stitching the top and bottom by sticking to both sides.

You might be able to add the extra ingredients after you've flattened the dough ball and still get a pocket (carefully making sure there is layer of clean dough between top and bottom).  Or go for reverse, take a look at this vegetable stuffed panbread which does not have any pockets but looks yummy none-the-less.

Otherwise, if you keep baking the wetness out, you might end up with a workable focaccia.  In general, adding wet ingredients to baked breads throws the formula out of balance.