Cover potatoes with salted cold water by 1 inch in a 4-quart saucepan, then simmer, uncovered, until just tender, 20 to 25 minutes. Drain in a colander and let stand until cool enough to handle, about 15 minutes. Peel potatoes and halve lengthwise.
Cook garlic in oil in a 12-inch nonstick skillet over moderate heat, stirring, until garlic is pale golden, about 2 minutes. Discard garlic, then stir potatoes and red pepper flakes into oil and sauté over moderately high heat, stirring occasionally, until potatoes begin to turn golden brown, 8 to 10 minutes.
While sautéing potatoes, cook zucchini in a pot of boiling salted water until just tender, 2 to 3 minutes, then drain in a colander.
Transfer potatoes with a slotted spoon to a bowl, then add zucchini to oil in skillet and sauté over moderately high heat, stirring, until hot, about 1 minute. Return potatoes to skillet and stir in salt.