What's the secret to making good turkish bread? (pide)
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.