In a small bowl, whisk together the ground flaxseed and water. Let sit for 5–10 minutes until thickened and gel-like.
In a large mixing bowl, add the corn, bell pepper, red onion, flour, baking powder, paprika, cumin, salt, black pepper, and the prepared flax egg. Stir until fully combined. The mixture will be thick and chunky.
Heat a thin layer of olive oil in a large non-stick skillet over medium heat. With wet hands or a spoon, scoop about ¼ cup of the batter and gently shape into a patty. Place it into the pan and lightly press to flatten.
Cook each fritter for about 4 minutes on the first side, or until golden and set. Flip and cook another 3 minutes on the other side, until browned and cooked through. Repeat with remaining batter, adding more oil as needed between batches.
(Optional): In a medium bowl, gently toss together the avocado, tomato, cilantro, and lime juice. Season to taste with salt and pepper.
Enjoy fritters warm or at room temperature, topped with avocado salsa if using.