Flynn was granted free agency by the Rangers on Tuesday.
Flynn was informed Friday that he won't be on the Rangers' 60-man roster, Levi Weaver of The Athletic reports.
Flynn was assigned to minor-league camp Wednesday.
Flynn signed a minor-league contract with the Rangers on Monday.
Flynn cleared waivers and was outrighted to Triple-A Omaha on Sunday.
Flynn was designated for assignment by the Royals on Friday.
Flynn (2-1) gave up seven runs on eight hits and no walks while striking out three through two innings to take the loss against the Tigers on Sunday.
Flynn is slated to start Sunday's game against the Tigers after Homer Bailey (undisclosed) was a late scratch, Lynn Worthy of The Kansas City Star reports.
Flynn was charged with three runs on seven hits and three walks over four innings of relief in Monday's 11-4 loss to the Blue Jays.
Flynn (elbow) was activated from the 10-day injured list Saturday, Rustin Dodd of The Athletic reports.