Will you accept a nice Gibraltar/Cortado? Any location of Coffee Commissary. If you need that texturized milk in there, try Coffee+Food on Melrose near Larchmont, Two Guns Espresso in Manhattan Beach, or Bronzed Aussie in downtown LA.
What's a flat white? It would appear by the responses that coffee is involved, but...... I have one low-fat latte in the early morning at Peet's Studio City, then no more coffee for the rest of the day, so all these other terms seem out there in left field.