Whisk together olive oil, orange zest and juice, lemon juice, rice vinegar, Dijon, honey, 1/4 teaspoon pepper, thyme, garlic, and kosher salt in a bowl until smooth and emulsified. Set aside. Remove and discard peel and white pith from oranges. Cut oranges crosswise into 1/4-inch-thick slices. Combine kale, endive, and spinach in a large bowl. Add vinaigrette; toss to coat. Transfer mixture to a large platter. Top with orange slices, onion, basil, cheese, currants, flaky salt, and remaining 1/2 teaspoon pepper.