Here you go
The NHL record for the most consecutive regular season overtime games is five, achieved by the Montreal Canadiens from October 27 to November 8, 1999. This is a team record, and since this is a relatively recent record, it is likely that there is no definitive individual record for most consecutive overtime games in a row. It's worth noting that the record for most playoff overtime games in a single season is 14, set by the Los Angeles Kings in 2013-14.
We have tied the record... 1 more to take it.