Pet form possibly from Fleming (man from Flanders) used as a feminine given name.
Flemmie is a pet form possibly derived from Fleming, itself a surname meaning a person from Flanders. That sort of transformation from surname to diminutive given name is a familiar pattern in English naming, where family names and nicknames often cross over into personal use.
Flemmie therefore begins in geography and identity, then softens into affectionate familiarity. As a given name, it has a vintage charm and a pleasantly informal feel. The -ie ending gives it a warm, approachable quality that makes it sound endearing and personal. Flemmie feels like a name with old roots and a friendly voice, preserving a trace of place history while becoming something more intimate.