Place the potatoes in a large pot, and add 1 tablespoon salt and enough cold water to cover. Cover the pot and bring the water to a boil over high heat. Then reduce the heat to medium-low and simmer until the potatoes are tender, 20 to 30 minutes, depending on their size.
While the potatoes are cooking, place the green beans, tomatoes, red onion, olives, parsley, capers, and red pepper flakes in a large mixing bowl, and stir gently to combine.
Combine the olive oil, lemon juice, and oregano in a small glass jar and seal the lid tightly. Shake the jar vigorously to combine. Season the vinaigrette with salt and pepper to taste, and set it aside at room temperature.
When the potatoes are tender, drain them immediately, and then let them cool until they can be handled. Cut the potatoes into small pieces, and add them to the bean mixture.
Pour the vinaigrette over the vegetables, and toss gently to coat thoroughly. Season with salt and pepper, if desired. The salad can be served at room temperature or chilled.
(It can be refrigerated, covered, for up to 3 days.)