Flannery reached the post-season for the only time in his career in . He made three plate appearances in the 1984 National League Championship Series and reached base all three times. Trailing 3-2 in game four of the series, Flannery hit a lead-off single in the fifth inning, and scored the tying run of the Padres' 7-5 victory over the Cubs. In game five, he reached on a ground ball that trickled through the legs of Cubs first baseman Leon Durham to score the tying run. In his only at-bat in the 1984 World Series, Flannery hit an eighth inning pinch hit single off Jack Morris in game four.