The Chiefs will make the playoffs.
Even though I think they they'll split the next two road games, let's assume they lose both and fall to 3-2. Then they get back-to-back home games against awful Jacksonville and even worse Buffalo. It's hard to envision the Chiefs finishing worse than 2-2 over the next four games.
Assuming they do, they'll be 5-2 and guaranteed the division lead through eight weeks of the season.
The next four games after that: @ Oakland, @ Denver, vs. Arizona, @ Seattle.
None of these teams are particularly good, but all of them—with the exception of the Cards—should have better than a 50% chance of winning. The Chiefs will be small underdogs in all three road games.
Let's assume the worst and say the Chiefs go 1-3 during this stretch.
That's 6-5 w/ 5 to play.
Of the next three games, the Chiefs are home to Denver, @ San Diego, and @ St. Louis. There is no reason why they shouldn't be able to take care of the Broncos and Rams. A loss to the Chargers is probably inevitable.
8-6 w/ 2 to play. The last two games are at home (Tenn, Oak).
Can't ask for much more than to have two games against mediocre teams at noisy Arrowhead to get you into the playoffs.