Preheat oven to 425°F (≈218°C). Line baking sheet(s) with parchment or spray lightly.
In a medium bowl combine black beans, chopped peppers, Mexicorn, green chilies, cooked chicken, both kinds of cheese, chili powder, cumin, salt, pepper, and red pepper flakes if using. Mix until evenly combined.
Lay one egg roll wrapper flat. Spoon about 3‑4 tablespoons of filling in the bottom third, leaving edges free. Fold sides over, then roll up tightly, seam side down. Place on baking sheet.
Repeat until all wrappers are filled or mixture is used (you may have leftover filling).
Brush tops of each egg roll with olive oil to promote crisping and golden color.
Bake in preheated oven for 15 minutes, until wrappers are golden brown and edges are crispy.
Serve warm with salsa, guacamole, or sour cream/Greek yogurt on the side.