In a large bowl, whisk together the gluten free flour, almond flour, baking powder and sea salt. Use your fingers to break up any clumps of almond flour.
Combine the coconut milk and apple cider vinegar, then pour the mixture over the dry ingredients. Stir until a soft dough forms.
Transfer the dough to a lightly floured piece of parchment paper. Dust the top with more flour. Form the dough into a disk—it should feel smooth but slightly tacky (although it shouldn’t stick to your hands). Divide the disk into 4 balls and refrigerate.
Preheat a 12-inch cast iron (or enameled cast iron) skillet over medium heat—let it get nice and hot.
Remove one piece of dough from the fridge (keep the rest of the dough refrigerated) and place it on a lightly floured piece of parchment paper. Dust the dough lightly with flour, then place another piece of parchment paper on top. Roll the dough into a ¼- to ⅛-inch thick oval. Peel off the top piece of parchment.
Spritz the hot skillet with cooking spray or coat it lightly with oil. Swiftly flip the dough (on the bottom piece of parchment) into the skillet. Peel off the parchment and cook until the bottom is golden and browned in spots, about 1-2 minutes.
Using a large spatula (or two spatulas), flip the bread over—the bread is tender and breaks easily, so be careful here (remember, if the bread breaks it’s no big deal—it will still taste delicious!). Cook until golden brown on the other side, about 1-2 minutes longer. Transfer to a cooling rack.
Repeat the steps with the remaining dough, being sure to flour the parchment paper and spray the pan between batches (if needed, use a damp towel to wipe out any browned flour in the skillet between batches). Keep your eye on the heat and adjust it as needed.
Let the flatbreads cool, then enjoy!