Three reasons come to mind why your bread may have turned out too hard-
1- If you didn't let it rise enough.
Flat breads often don't have a proofing step. The dough should double in size on the first rise and then after you divide the dough let it rest to make rolling out easier.
2- Working the dough too much without resting.
When rolling or stretching the dough be gentle. You don't want to force all the air out. If you do think that you overworked it, letting it rest for a while will let the yeast work a little more.
3- Too low of oven temperature
Traditional flat breads are often baked in large, wood-fired, brick ovens. Your recipe calls for 475F and I would say that that would be a lower bound. Since flat breads are so thin they dry out quickly. In general the hotter you can bake them the better. Try throwing a couple loaves on a very hot grill but indirect heat. Expect this to take less baking time than your recipe. If you get some charring that is ok and even desirable. If you get charring that goes all the way through then you rolled the loaves a little too thin.
Personally- I am skeptical of the milk basting. This would keep the surface of the bread moist but it would cool down the oven which would be horrible for the bread. I never saw turkish bakers basting their flat bread but maybe it is a regional thing.
Kneading dough has a few functions. First, it distributes the ingredients together evenly and allows the flour to become hydrated. As the flour starts to absorb water, enzymatic reactions occur and some proteins begin to mesh together. The two most important in this process are glutenin and gliadin. When these proteins start to get tangled up together, they form gluten, which is the protein that allows bread dough to stretch and trap gas bubbles produced by yeast. These reactions will occur on their own to an extent, as in no-knead recipes, but kneading accelerates the process.
Kneading also allows you to control the texture of the bread. A vigorous knead can help to produce a bread with a fine crumb as the kneading an tighten the gluten, keeping the air bubbles more uniform. Doing short kneading periods (or folds) spaced by time for the dough to relax and rise can give you more extensible dough which can help give you a more open crumb structure.
Finally, kneading is sometimes used to add inclusions to the dough that would disrupt it's activity if added to early. This can be things like seeds, which would cut gluten strands if included too early in the process, or things like butter in a brioche, which would shorten the dough if included before the gluten had already developed.
Best Answer
If you punch down a no-knead loaf, on average, you'll get a more consistent crumb and fewer large holes in the finished loaf.