Preheat grill to medium-high, or preheat the oven to 425º. Or place on outer edge of campfire, being careful not to let burn.
In a medium-sized bowl, toss potatoes with olive oil, garlic powder, and oregano and season with salt and pepper. Add red pepper flakes, if using.
Divide potatoes between two large foil pieces, then fold the foil packets crosswise to completely cover the potatoes. Roll the top and bottom edges to seal them closed.
Place foil packets on the grill and cook until just cooked through, 10 to 15 minutes. (Or transfer to the oven and bake about 15 minutes.). Campfire cooking times will vary. You can open the foil packet to test the softness of the potatoes, and then reseal to continue cooking, if needed.
Unwrap the foil packets and sprinkle both types of cheese on top of the potatoes. Fold foil back over the potatoes and cook until cheese is melty, about 3 to 5 minutes.
Allow to cool slightly before unsealing and serving.