Bring a large pot of lightly salted water to boiling. Heat bacon in a large nonstick skillet over medium heat. Cook 8 minutes, until crisp. Remove to paper towels with a slotted spoon.
Add olive oil and garlic to skillet. Cook 2 minutes, stirring so garlic doesn't burn. Stir in spinach and cook 3 minutes.
Meanwhile, add spaghetti to boiling water. Cook 6 minutes and drain. Return to pot.
Stir clams with their juice and pepper flakes into skillet with spinach. Cook 3 minutes. Add spinach mixture to pasta along with lemon juice. Toss to combine; serve with lemon wedges on the side.