Process olive oil and chives in a blender until chives are pureed; set aside.
Stir together shallots and next 3 ingredients. Pour over red and yellow tomato slices; toss gently. Set aside.
Place cheese and milk in a large bowl; mash with a fork. Stir in onion.
Place bottom slice of red or yellow tomato on a serving plate. Spread about 2 tablespoons of feta mixture over slice; drizzle with about a teaspoon reserved chive oil. Repeat with middle slice of tomato, feta mixture, and chive oil. Top with stem end of tomato. Repeat with remaining tomatoes, feta mixture, and chive oil. Drizzle tomatoes with remaining shallot marinade and chive oil.