Make the tomato water: Combine tomatoes and salt in a blender and process until smooth. Set a fine mesh strainer lined with a double layer of cheesecloth over a medium bowl, pour on the blended tomatoes, and refrigerate. The next day the hung mixture should yield about 1⁄2 cup tomato water.
Tomato water vinaigrette: In a medium bowl, add all ingredients, and whisk to combine. Set aside.
To make the salad: Rub the whole tomatoes and diced cucumbers with a small amount of oil to barely coat. Heat a grill to high and grill tomatoes over direct heat until charred but not mushy, about 2 minutes. Place cucumbers in a grill basket and grill over direct heat, about 2 minutes. Dice the tomatoes and combine with the grilled cucumbers, and transfer to a medium bowl. Add herbs, greens (if using), chives, chili flakes, and vinaigrette, stir to combine, and marinate in the refrigerator 1–3 hours. Season to taste with salt, toss, and serve.