Answer:
A young woman who embraced new fashions and new attitudes of the day.
Explanation:
The word "flapper" is a noun that refers to a woman or a young person of the female gender intent on enjoying her life as she sees fit. She does not care about what society thinks or feels and her focus is on herself.
In the given excerpt from Agatha Christie's The Murder on the Links, the speaker talks about how she detests modern girls "who jazzes from morning to night, smokes like a chimney, and uses language which would make a billingsgaté fishwoman blush!" This is exactly what a "flapper" is, a young woman who cares nothing except for her own enjoyment.
Thus, the correct answer is the first option.