The MLB manager that has won the most consecutive Pennants in the American League was Casey Stengel. He has won 5 Pennants. New York Yankees (1949-53).
The MLB manager that has won the most consecutive Pennants in the National League was John McGraw. He has won 4 Pennants. New York Giants (1921-24).
The MLB manager that has won the most consecutive Pennants in the American Association was Charles Comiskey. He has won 4 Pennants. St. Louis (1885-88).