In the Kansas City Chiefs' first preseason game, the starters played about a quarter and a half (little more than that). In their second preseason game, they played the first half.
In the third preseason game, they played three full quarters.
Don't expect this trend to continue. Historically the fourth preseason game you only see the starters play a couple of series, if at all.
The third preseason game is when the starters will play quite a bit. This is because any minor injuries sustained in the third preseason game would give you over two weeks to prepare for the regular season opener.
Teams don't want a player in the fourth preseason game to suffer something minor like a sprained ankle that would prevent them from playing at 100 percent in the regular season opener.
So don't expect to see much from the starters. My guess is that in Kansas City they won't even make it through the entire first quarter.