The Kansas City Chiefs were indeed not awarded any compensatory draft picks by the NFL, which handed out picks today to certain teams for their transactions in unrestricted free agency last year. The Chiefs signed far more players than they lost last year, so it wasn't a surprise they were shut out.
But the Chiefs should receive picks next season based on this year's activity in unrestricted free agency. The NFL will no doubt see what the Chiefs lost (Dexter McCluster, Branden Albert, Jon Asamoah, Geoff Schwartz, Tyson Jackson, Akeem Jordan, Kendrick Lewis, Quintin Demps) is greater than what they gained (Vance Walker, Jeff Linkenbach, Joe Mays, Chris Owens).
That doesn't help the Chiefs this year, of course. It's a deep draft but the Chiefs will have only one of the top 86 picks. Their second-round pick is in the possession of the San Francisco 49ers. The pick went to San Francisco as part of last year's Alex Smith trade.
That's why the Chiefs need to be aggressive when it comes to trading for additional picks.
As a reminder, the Chiefs have six picks this year. They have their own pick in the first, third, fourth, fifth and sixth rounds. They have an additional pick in the sixth round that came from the Dallas Cowboys as part of last year's trade that sent Edgar Jones to the Cowboys.
The Chiefs have no pick in the second or seventh rounds. Their seventh-round pick went to the Cowboys as part of the Jones trade.