Whisk together eggs, milk, chives, basil, pepper, and salt in a bowl.
Heat oil in a 12-inch ovenproof nonstick skillet (if handle is plastic, wrap it in a double layer of foil) over moderate heat until hot but not smoking. Pour egg mixture into skillet and scatter cream cheese pieces on top, then cook, lifting up cooked egg around edges using a spatula to let raw egg flow underneath, until frittata is set on bottom and egg is almost set but still moist on top, 3 to 5 minutes. Remove from heat. Sprinkle salmon all over frittata, then press on salmon lightly and shake skillet to allow salmon to settle into top.
Broil frittata about 6 inches from heat until set, slightly puffed, and golden in patches, 1 to 1 1/2 minutes.
Cool 5 minutes, then loosen edge with spatula and slide onto a large plate. Cut into wedges and serve warm or at room temperature.