As a "wedding present" to Lady Felicia, Flambeau gifts her the necklace he 'acquired' from the hotel safe of Nicholai Solovey (Mark Umbers) in Series 7 Episode 10 Father Brown: The Honourable Thief.
When Flambeau and Lady Felicia are telling Lady Cecily about how they met, they are correctly recalling their first on-screen meeting as shown in Series 3 Episode 10 Father Brown: The Judgement of Man.