Flagg, a 19-year-old American who has scored 20.4 points and grabbed 6.4 rebounds a game for the Mavericks so far this season, is out with a left foot sprain.
He was ruled out of Dallas' game at the Los Angeles Lakers on Thursday after suffering the injury in a Tuesday loss at Phoenix.
Washington center Sarr was ruled out because of a right hamstring strain.
The Rising Stars competition, part of NBA All-Star weekend at Los Angeles, features a four-team tournament involving three squads of rookies and second-year players coached by former NBA stars Carmelo Anthony, Tracy McGrady and Vince Carter plus a developmental G-League club guided by Austin Rivers.
Utah Jazz rookie forward Ace Bailey and Washington Wizards guard Bub Carrington were named injury replacements, Bailey taking Flagg's spot on Anthony's team and Carrington replacing Sarr in McGrady's lineup.
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