Using a box grater or shredding blade of a food processor, shred the potatoes. Rinse until the water is clear. Drain. Dump the shredded potatoes onto a clean kitchen towel. Squeeze to remove all excess water. Add the shredded potato into a large mixing bowl along with the flour and eggs. Mix well.
Cook the chorizo in a large nonstick skillet over medium heat, breaking any lumps, until it begins to crumble and is cooked through. Add the onions and saute until translucent, about 3 minutes. Season with salt and pepper. Add the chorizo-onion mixture to the shredded potatoes. Mix to combine.
Heat about 1/4 inch of oil in a large, heavy skillet over medium-high heat. When the oil is sizzling hot, place the mixture in separate piles like pancakes. Cook until nicely browned on the bottom, then flip over and brown on the other side. It should take 3 to 5 minutes per side. Transfer hash browns to a paper-lined plate and drain. Season with 1/2 teaspoon pepper and serve immediately.