I can say this about former Chiefs GM Scott Pioli: he was good at massaging the salary cap. The Chiefs have hardly any "dead money" and very few (if any, really) bad contracts. They're in good shape with plenty of their young stars signed long-term.
There are a couple of notes on the future of the team regarding the salary cap.
First, teams are being told the cap will be around $121.1 million, which is close to what it was last year, according to Ian Rapoport of NFL Network. I don't know if it was intended to stay flat for a couple of years but supposedly the new TV money coming later in the life of the CBA will increase the salary cap. I know nothing about the league's finances and don't try to understand it. More money for the league = teams spending more money eventually. That's all I know.
Second, the Chiefs are believed to have roughly $13.3 million in salary cap space. ESPN's John Clayton reported last month that the Chiefs had $16 million in salary cap space but the NFL Network puts it at $13.3 million today. The Chiefs have made a handful of minor personnel moves in the last month and more will be coming. For example, Matt Cassel ($7.5 million) or Tyson Jackson ($14.72 million) could both be gone, so these numbers will change quite a bit.
On another note...
Somehow, the NFL and NFLPA produce different cap numbers when you ask them, which makes things confusing as hell for the fans. Different numbers get reported. Teams claim the reported numbers aren't accurate. The players' agents do the same. It's all a big mess and it's a reason why the league needs to make a legitimate source for the salary cap publicly available.
The Chiefs may have to spend some of that money on a cornerback. BJ Kissel takes a look at that position in the video below: