In a medium bowl, blend flour, cornmeal, rolled oats and apple flakes together until incorporated; set aside.
In a separate bowl, blend eggs, apple puree, Canola oil, peanut butter, and vanilla extract together until incorporated.
Stir the dry ingredients into the wet ingredients and mix until a uniform dough forms.
On a floured surface, roll out the dough to ¼ inch thickness and cut into bone shapes.
Bake on parchment-lined sheets for 15-20 minutes at 350ºF.
Turn off the oven and allow the treats to cool completely, until crisp and hard.