To make the feta-chive salad dressing, combine feta cheese, buttermilk, greek yogurt, lemon juice and chives in a medium bowl, gently stirring to combine. The dressing should still have some bits and chunks of feta showing. Season to taste with kosher salt and black pepper. I didn't add any additional salt, but you may want to. Store in the refrigerator until ready to use.
Cut watermelon into thick wedges, then arrange on a large platter. Also cut tomatoes into smaller wedges, and scatter over the watermelon.
To serve, dot the wedges of watermelon and tomato with the feta-chive dressing. Sprinkle with chopped chives, basil and a little flaky sea salt. Transfer extra dressing to a small bowl and serve beside the salad.