In a small bowl combine sour cream, garlic, cilantro, and salt. Reserve half of the mixture for dipping. Place the remaining mixture in a shallow dish and whisk in milk until combined. In another shallow dish combine crushed potato chips, thyme, black pepper, and cayenne pepper. Place flour in a third shallow dish.
Dip tomato slices in flour, turning to coat; shake off excess. Dip in sour cream-milk mixture, then in potato chip mixture.
In an extra-large skillet heat 2 tablespoons of the butter and 2 tablespoons of the oil over medium heat. Add half of the coated tomato slices; cook about 4 minutes or until crisp and golden, turning once halfway through cooking. Drain on paper towels. Add remaining butter and olive oil to skillet. Add remaining tomato slices; cook as above. Serve with reserved sour cream mixture.