Preheat the oven to 350 degrees F. Generously oil a 9-inch skillet; set aside. Whisk together the nut milk and chia seeds in a medium bowl to combine; set aside.
Grind the corn grits in an electric spice grinder until they're the texture of cornmeal, and add them to another medium bowl. Sift in the oat flour, millet flour, brown rice flour, arrowroot and baking powder, and stir well.
Add the squash, oil, salt, maple syrup, 1/4 cup water and scallions to the chia mixture, and whisk to combine. Add the chia mixture to the flour mixture, and stir until just combined. Scrape the dough into the prepared skillet, and gently flatten to fill the pan.
Bake the cornbread until a toothpick comes out clean, 28 to 30 minutes. Let cool for 15 minutes. Run a knife around the edge; place a plate over the skillet, and invert. Slide the cornbread back into the pan with the bottom facing up (to show off the beautiful crust). Serve warm.
Instead of corn grits, you can use the same amount of regular cornmeal if you have it on hand.