In a small bowl, whisk together the white wine vinegar, sugar, 1 teaspoon of the salt, the black pepper, and the red pepper flakes until the sugar has dissolved.
Add the red onion and let the mixture stand for 1 to 2 hours. Drain the red onion, discarding the liquid.
Make one large salad in a salad bowl or make individual salads by gently combining the red onion, cucumber, watermelon, and feta.
Season with the remaining 1 teaspoon salt and lightly drizzle with the olive oil and balsamic vinegar. Garnish with chopped mint.
Adapted from Gumbo Love by Lucy Buffett (Grand Central, 2017