Preheat oven to 350°F. Brush the edges of four 6-ounce ramekins with melted coconut oil or spray them with cooking spray.
Place oat flour and solid coconut oil in a medium bowl.
Using a fork or your hands, work the coconut oil into the flour until it is crumbly.
Add water and combine well until a dough forms.
Place the dough on a floured surface and roll out the dough until it is ¼ inch thick.
Place a ramekin upside-down onto the rolled-out crust. Cut a circle around it that is ½ inch wider so the crust will overlap the ramekin edge. Repeat to make 4 top crusts.
Combine chicken, vegetables, water, and oat flour in a bowl. Evenly divide the mixture between the ramekins. Put the ramekins on a baking sheet.
Lay the crust over the top and pinch the crust along the edges of the ramekin to seal it.
Using a knife, cut an X or cross shape in the crust to allow steam to escape.
Bake for 35 to 40 minutes until the crust is browned.
Allow the pies to cool completely to room temperature before serving.