Just did a bit of unscientific research: of the seasons we have (S18-present), I couldn't find anyone with a longer win streak. S21 Toronto also had 22 wins in a row but some came in OT/SO (Quebec this season is currently on 22 consecutive regulation wins).
I would have to imagine 69-3-0 Calgary from S1 beat it, unless they were really unlucky with where their 3 losses fell. If not them, then one of the other beast early day teams (S3 CGY, S5 SEA, S11 DAV).
But modern era record looks like? Awoooooooo
(In addition to S21 Toronto I looked at S19 Calgary, S27 Seattle, S32 Riga (19 wins to start the season), S33 Helsinki, a couple recent NY teams)