There has been only one World T20 innings that a team has registered a record six ducks. It happened in the 2007 edition when Kenya were bowled out for 73. Kenya lost their top four batsmen for ducks and had two more ducks in the line-up. New Zealand chased down the target comfortably by 9 wickets.
There was another incident in T20Is that a team registered six ducks. It happened in a one-off T20I between Zimbabwe and West Indies at Port of Spain in 2010.
Batting first, Zimbabwe were reduced to 3/0 and lost more three batsmen for ducks, but posted what turned out to be a match-winning total of 105. Zimbabwe won by 26 runs as West Indies were bowled out for 79.