A Member of the Wedding (1951) has only been released on dvd as one of 5 films on the Stanley Kramer Film Collection (Guess Who's Coming to Dinner / Ship of Fools / The Member of the Wedding / The Wild One / The 5,000 Fingers of Dr. T) single-disc release, which Netflix does not carry, but you can purchase it at Amazon.
Besides, Julie Harris strains credibility to the extreme in that film, for me it ruined the experience. It's certainly a fine picture — Fred Zinneman didn't make too many bad ones, but a 27 year old playing a 12 year old is hard to swallow. Yikes.