In food processor, finely grind almonds. Add garlic, tomatoes, vinegar, pepper flakes, and salt, and purée until paste forms, scraping down sides occasionally. Add parsley and with motor running, slowly add oil.
In large bowl, mix together flour, salt, and pepper. In 4-quart deep, heavy pot over high heat, heat 2 inches oil until deep-fat thermometer registers 350°F.
Dredge half of anchovies in flour mixture, tossing to coat well. Transfer to sieve and shake to remove excess flour. Fry, stirring frequently to separate, until golden, about 3 minutes, then transfer with slotted spoon to paper towels to drain. Repeat with remaining anchovies, returning oil to 350°F between batches.
In small nonstick skillet over moderate heat, melt butter. Crack egg into pan and cook until white is firm and opaque, but yolk is still runny, 2 to 3 minutes. Transfer with slotted spatula to paper towels to drain. Keep warm.
Arrange anchovies on platter and sprinkle with lemon juice. Top with fried egg and serve with Salbixtada sauce alongside.
