Preheat oven to 400°F. Line a large baking sheet with parchment paper.Mix the ground flax and water in a small bowl and set aside for 5 minutes or so to thicken.Combine all ingredients together in a large bowl, including the flax mixture and the 1.5 cups cooked quinoa. Stir well until the mixture comes together. Don't forget the flour because it helps bind the patties.Shape mixture into 1/4-cup patties with wet hands. Pack tightly so they hold together better. Place on baking sheet.Bake for 15 minutes, then carefully flip cakes, and bake for another 8-10 minutes until golden and firm.Cool for 5 minutes on the sheet and then enjoy!Store leftovers in a container in the fridge for up to 5-6 days. To reheat, preheat a skillet over medium heat, add a bit of oil, and cook patties for about 3 minutes per side, or until heated through.