Bring a large pot of heavily salted water to a boil. Add the farro and cook until tender, about 30 minutes. Drain, spread out on a baking sheet and let cool.
Combine the cucumbers, cantaloupe, tomatoes and farro in a large serving bowl; set aside.
Whisk together the olive oil, vinegar, shallots, 2 teaspoons Kosher salt and several grinds of pepper in a medium bowl until emulsified. Pour the vinaigrette over the salad, add the feta, mint and chives or green onions and gently toss until the salad is evenly coated. Serve chilled or at room temperature.