Lol. According to the Braves page on mlb.com, they have played the Dodgers twice in the postseason, winning 3-0 in 1996 and losing 3-1 in 2013.
It's funny, because I have the exact inverse of your sentiment. When the Dodgers and Braves were in the NL west and the Braves were on their run in the 90s, it seems like there were several years where the division winner wasn't determined until the final weekend of the season, and the Braves always pulled it out. I still hate it when they play, because I always expect the Braves are going to win the series (regular or post season).
Edit: And history has obviously been unkind to my memory as well

There was actually only one year (1991) where the NL West came down to the Braves or Dodgers, with Atlanta winning the division by one game that year.