Most consecutive football league wins at start of season?

The New England Patriots had won 21 in a row if you include regular and post season -2003-2004 season.

Regular season only The New England Patriots have 18 Consecutive wins in the 2003-2004 season

Chicago Bears had 18 regular season straight wins 1933-34 & 1941-42 as well as;

Cleveland Browns had 18 -1947-48

Miami Dolphins had 18 -1972-73

San Francisco had 18 -1989-90

Denver Broncos had 18-1997-98