Dickey was the Braves' most consistent starter this season, going 10-10 with a 4.26 ERA in 31 starts. He said at the end of the season he will meet with his family before deciding whether he wants to pitch in 2018.
He gets a $500,000 buyout and becomes eligible for free agency.
Flowers, 31, will return for his third season with Atlanta after hitting a career-best .281 with 12 homers and 49 RBI. He had arthroscopic surgery on his left wrist Oct. 9 and is expected to be ready for spring training.
Flowers and Kurt Suzuki combined to give the Braves 30 homers and 98 RBI at catcher last season. Suzuki agreed to a $1.5 million, one-year contract for 2018 on Sept. 23.
The Braves made the announcements Monday.
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