IIRC, i think the great Vince Lombardi GB Packers did win 3 NFL championships in a row.
The Packers have done it twice. 1929-1931. And 1965-1967. Of course, those 1929-1931 championships were determined by record rather than playoffs. And the 1965 championship was the year before the first Super Bowl. So, while the Packers HAVE won the NFL championships three times in row, twice, they have only won 2 Super Bowls in a row — no one has ever “three-peated” Super Bowls.
The Packers did win three championships in a row but that was before the merger between the NFL and AFL.
That is now the chink in the armor of the NFL so that now they say. “No team has won three in a row,” with the caveat, ‘since the merger.’