Heat the oil in a medium saucepan (ideally cast iron or non-stick) over medium-high heat. Add the red pepper and saute a minute or so. Add the zucchini and saute until just tender.
Drop the heat to medium-low and add the eggs and chives to the pan. Scramble with the vegetables until cooked.
Lay 2 slices of cheese on the center of each flatbread and microwave on high until melted.
Spoon the egg mixture onto the flatbreads and roll up like a burrito.
Serve warm. See notes for freezing instructions.
To freeze, let cool, wrap in plastic and store in a ziplock freezer bag. To reheat, put straight from freezer to microwave and heat on high until warm.