Preheat the oven to 400°F (200°C) and line or grease a baking sheet.
Fit a food processor with the grating disc. Cut the sweet potato and 1/2 red onion into large chunks and grate them in the processor; transfer the shredded vegetables to a bowl or set aside.
Replace the grating disc with the standard S-blade. Add the oats, ground flax seed, garlic powder, ground cumin, and kosher salt to the processor and process until a fine flour forms, about 30–45 seconds.
Add 1 can of drained black beans, the chipotle peppers, 1 tablespoon adobo sauce, and avocado oil to the processor; process until a thick paste forms, about 1 minute, scraping down the sides as needed.
Return the shredded sweet potato and onion to the processor along with the remaining can of drained black beans. Pulse until the mixture holds together and is mostly combined, pausing to scrape and mix with a spatula as needed.
With slightly damp hands, portion the mixture using a 1/2-cup measure to form 8 even patties. Flatten and smooth each patty and place them on the prepared baking sheet.
Bake on the middle rack for 20 minutes. Flip the patties, move the sheet to the top rack, and bake an additional 15–20 minutes until set and lightly crisp. Let the patties rest on the baking sheet 5–10 minutes to firm up.
Serve the burgers warm on toasted buns with chipotle mayo, sliced red onion, lettuce, avocado, or other desired toppings.