OKC and Spurs are the only teams to not lose 3 games in a row this season
Every other team has lost 3 or more games in a row this season, except the OKC and Spurs, both of which have only lost 2 in a row at most. With 2 games remaining for both, and having won their latest games, they have clinched a 2-game losing streak as their longest losing streaks.
I didn’t find any official stat for this to use as a source, you just have to go through each team’s schedule to count their losing streaks.
Spurs schedule: https://www.nba.com/spurs/schedule?EventSchedule=3
OKC schedule: https://www.nba.com/thunder/schedule?EventSchedule=3