Bring a large pot of salted water to a boil. Add brussels sprouts and cook just until tender and bright green, about 5 minutes. Drain and set aside.
Meanwhile, blot capers on a paper towel. Heat oil in a large frying pan over high heat. Add capers and cook, stirring carefully (mixture will splatter), until capers start to open and are brown and crisp, about 5 minutes. With a slotted spoon, transfer capers to a paper towel to drain.
Add garlic and anchovies to pan and cook until fragrant, about 1 minute. Add brussels sprouts and chile flakes and stir to coat with oil. Cook, stirring occasionally, until starting to brown, about 5 minutes. Transfer to a serving plate and sprinkle with capers and a squeeze of lemon.
Note: Nutritional analysis is per serving.