Outplayed by undrafted rookie Albert Wilson while battling through a nagging, season-long groin injury, Avery appeared in just six games last year.
The brittle speed merchant totaled 772 yards and a pair of touchdowns on 55 receptions in two seasons with the Chiefs after signing a three-year, $8.55 million contract in March of 2013.
Jenkins, the 49ers' No. 30 overall pick in 2012, is one of the biggest draft busts in recent memory. He has managed a paltry 17 receptions for 223 yards in three NFL seasons under Jim Harbaugh and Andy Reid, two of the most respected offensive coaches in the game.
To put the lack of production in perspective, Kansas City became the first team since the 1970 NFL-AFL merger without a single touchdown by a wide receiver.