Line a 9" x 5" loaf pan with plastic wrap, letting at least 4" hang over the edges; set aside. Bring beef, pork, stock, salt, and 4 cups water to a boil in a 6-qt. saucepan over high heat. Reduce heat to medium-low; cook until meat is very tender, 1½-2 hours. Strain meat, reserving ⅓ cup of cooking liquid. Transfer meat to a food processor; pulse until finely ground and set aside.
While meat is cooking, bring 3⅓ cups water to a boil in a 4-qt. saucepan over high heat. Stir in oats and salt; reduce heat to medium and cook, stirring occasionally, until oats are tender, about 15 minutes. Transfer oats to a food processor; add meat, reserved cooking liquid, onion flakes, white pepper, and salt. Purée until mixture becomes a thick paste. Press into loaf pan and fold excess plastic wrap over top; refrigerate overnight.
To serve, heat oil in a 12" cast-iron skillet over medium-high heat. Unwrap goetta and slice crosswise into ½"-thick pieces. Working in batches, fry slices, flipping once, until crisp and browned, 4-5 minutes.