Heat vegetable oil in a small skillet over medium heat; cook and stir garlic until softened and lightly browned, about 5 minutes. Set garlic aside to cool.

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Whisk vinegar and sugar in a salad bowl until sugar has dissolved; add chili-garlic sauce, fish sauce, coriander, cooked garlic, and red pepper flakes until thoroughly combined. Stir in cucumbers, peanuts, and green onions to coat with dressing. Refrigerate at least 1 hour to overnight.