Came across a very interesting article by Chase Stuart of the Ny Times (see link at end for whole article). A brief summary of the article is as follows.
A total of 108 teams, including three this year, have started 3-0 since 1990. But the Chiefs are just the sixth team to do so after winning no more than four games the season before (last year the Chiefs were 4-12).
In Stuart's article he points out the fates of the other 5 teams:
2006 Saints - after going 3-13 in 2005 the next year they went 10-6, got to the NFC championship game and then three years later went to the Super Bowl
2002 Panthers - Carolina was dismal in 2001 when they went 1-15 but in 2002 they improved to 7-9 and then in 2003 they went to the NFC Championship game
2001 Chargers - Chargers are one exception they went 1-15 in 2000 (with Ryan Leaf) then started 3-0 the next year but ended up 5-11 but they got LT in the draft
1999 Rams - After a 4-12 season in 1998 the Rams assembled the Greatest Show in Turf and in 1999 won the Super Bowl
1995 Rams - 4-12 in 1994 ended up 7-9 in 1995
Check out the whole article (highly recommended here)