Heat lemon juice in a saucepan over medium heat until just simmering. Whisk in butter one piece at a time until combined and emulsified (4-5 minutes, do not boil). Add celery, capers and chives and stir to combine, season to taste and keep warm.
Heat olive oil in a large frying pan over high heat. Dust fish in seasoned flour, dusting off excess, add to pan and cook, turning once, until golden and crisp (3-4 minutes each side). Transfer to serving plates, spoon over sauce and serve hot with zucchini flowers.