Preheat the oven to 350 degrees.
Bring a pot of salted boiling water to a boil. Cook the potatoes until tender then drain well.
Heat a saute pan on medium heat. Once hot, add the oil (reserve 2/3 of the oil for the eggs). Saute the chorizo until nicely browned, then add in the potatoes and continue to sauté browning the potatoes. Season with salt and pepper to taste.
Place the flatbread on a baking sheet and top with cheese evenly. Bake in the oven to melt the cheese, about 2 to 3 minutes.
Preheat a non-stick pan over medium low heat. Add the remaining oil. Crack eggs on a flat surface and into the pan being careful not to break the yolk. Cook until the whites of the eggs start to become firm, add 1 to 2 tablespoons of water and cover with a lid to help firm the whites quicker. Season with salt and pepper.
Serve the eggs on the flatbread. Top with chorizo potato mixture. Garnish with tomato, cilantro, and jalapeño. Serve with orange.