Flynn was granted free agency by the Rangers on Tuesday.
Flynn signed a minor-league deal with the Rangers in December as a non-roster invitee, but he was left off the roster for the team's summer camp and was granted his release Tuesday. The southpaw made 11 appearances (one start) with the Royals last season, posting a 5.22 ERA and 1.88 WHIP over 29.1 innings.