Probably the streakiest. They lost their first three series after moving to Minnesota (1965, 1969, 1970), then won their next five (1987 (ALCS/WS), 1991 (ALCS/WS), 2002 (ALDS)), and have now lost their last 9 (2002 ALCS, 2003 ALDS, 2004 ALDS, 2006 ALDS, 2009, ALDS, 2010 ALDS, 2017 WC, 2019 ALDS, 2020 WC). In their 12 playoff series losses, they failed to win a game 8 times, and won only one game 3 times.
Overall, since moving to Minnesota, the Twins are 25-45 (.357). I'm not sure if that is the worst, but I would imagine it is in the bottom quarter.