I don’t think a flavor will work for you Mario. At the high temperatures in the pita oven flavors flash off and nothing is left.
In the middle east milk is not usually used in pita breads, but from what I understand the texture you are after is what you are wanting in your region. For your milk replacement I would likely start with soy flour and lecithin, or lecithinated soy flour, if a single ingredient is more manageable. When we ask ourselves why the milk is in there, it is likely mostly to promote emulsification, maillard browning, and richness in flavor. Other things to consider are nut butter. Cashew butter or blanched almond butter will help without adding too much nutty flavour. Adding mono and diglycerides, if possible, may also help with keeping the pita plyable.