Nowhere in Sydney is flat in a Southerly. Georges River is about as flat as you'll find though and even that can have waist high chop in the middle. There can be quite a lot of tidal flow with Georges River, so keep that in mind. It's best in SW, but okay in a Southerly. No good in a SE though. Launch from Riverside Drive near St George Sailing Club. Other than that your only other option is Brighton Le Sands at Bestic Street in a S or SE.
You can try gunnamatta, but I would guess it's way too busy with boats and the ferry. It would also be extremely gusty (if at all windy) and horrible. The runs would be very short.
There's really not many options in a Southerly. Like Geewiz

says, a lot of keen Sydney sailors travel to Budgewoi or Canton, North of Sydney, where it's pretty shallow and a lot flatter. Primbee, on lake Illawarra, is fantastic in a Westerly and well worth the drive.