Combine non-dairy milk with apple cider vinegar. Stir and set aside.
Combine the flaxmeal with water. Stir and set aside.
Let both mixtures sit for 5 minutes before using.
In a large bowl, combine cornmeal, flour, sugar, baking powder, salt and cayenne pepper. Whisk together to mix.
Add the grated onion, buttermilk mixture and flax egg. Fold together with a spatula until all of the dry ingredients are incorporated. Let the batter rest while you heat the oil.
Heat about 1 quart of oil in a large skillet over medium high heat until the oil reaches 350-375ºF (176-190ºC). Place a wire rack over a baking sheet and set it aside.
Using two teaspoons, scoop a ball of the hushpuppy batter in one spoon and use the second spoon to scrape it off into the oil. Add about 6-7 hushpuppies to the oil at a time, being careful not to crowd your pan or cool the oil temperature.
Fry for 3 minutes, while flipping once or twice.
Remove from the oil and transfer to your wire rack to drain. Repeat with the remaining batter.
Serve immediately.