Beat eggs and red pepper flakes together in a bowl. Stir tomatoes, feta, and basil leaves into egg mixture.
Heat olive oil in a nonstick skillet over high heat until oil starts to shimmer. Pour egg mixture into hot oil and cook, without stirring, for 5 seconds.
Cook and stir egg mixture until eggs are scrambled and softly set, about 30 seconds. Transfer eggs to a plate and sprinkle with sea salt.
