In a small bowl, combine ricotta, Greek yogurt, lemon zest, lemon juice, salt, and black pepper. Whip until smooth, glossy, and airy. Set aside.
Place the drained crab meat in a bowl and gently loosen the lumps, keeping the texture intact. Drizzle with olive oil, add lemon zest, salt, and chili flakes. Toss very gently just until coated.
In a separate small bowl, mix olive oil and finely minced chives. Lightly crush the chives with a spoon to release their flavor and color, then let rest for 5 minutes.
To assemble, spread a generous layer of lemon ricotta cream over each toasted baguette slice. Top with dressed crab, then finish with a light drizzle of chive oil. Serve immediately.