The 2018 campaign will mark Flowers' third with the Braves and his 10th in the majors. He batted a career-best .281 with 12 home runs and 49 RBIs in 99 games this season.
In his two seasons since joining Atlanta as a free agent, the 31-year-old Flowers is hitting .276 with 20 homers and 90 RBIs over 182 games.
Flowers, 31, underwent arthroscopic debridement surgery on his left wrist on Oct. 9. He is expected to be fully ready for the start of spring training.
Flowers shared catching duties with Kurt Suzuki, who signed a one-year contract extension on Sept. 23.
Dickey, 42, just completed his 15th major league season, going 10-10 with a 4.26 ERA in 31 starts in his lone year with the Braves. He made his 300th career start and 400th career appearance in his final turn of the season on Sept. 26.
Dickey reached the 30-start mark in six of the last seven seasons, dating to 2011, and the knuckleballer owns a career record of 120-118 with a 4.04 ERA in 2,073 2/3 innings pitched.