In the bowl of a food processor, combine the rolled oats, drained and rinsed chickpeas, and fresh dill. Pulse for 5 seconds. Add the white vinegar then continue to blend until the mixture appears finely chopped and sticks together when you press it between your fingers. Scoop the mixture out into a large bowl and set aside.
Next add the onion, garlic cloves, and beets to the food processor then blend until finely chopped. In large skillet, warm the oil over medium heat. Add the beet mixture from the food processor, sprinkle with a teaspoon of salt and cook for about 5-7 minutes, until soft. Transfer the mixture to the bowl with the chickpeas.
Add the chickpea flour to the bowl and stir together until well-combined. If the mixture appears too wet, add more flour (1 tablespoon at a time) until it's dry enough to hold together. Scooping out about 1/4 cup of the mixture at a time, use your hands to form individual patties. Cook them in the greased skillet over medium heat for about 4 minutes on each side.
Meanwhile make the tzatziki by combining everything in a small bowl. Stir together until well-combined. Serve the patties warm topped with tzatziki and enjoy!