I interpret it to mean surpass. Jump is commonly used to describe some kind of rise or increase:
b. To rise suddenly in position or rank: jumped over two others with more seniority.
In sports, a depth chart is used to show the placements of the starting players and the secondary players. Generally a starting player will be listed first or on top while a back-up will be listed below. Depth charts also tend to resemble the actual position locations of certain players.
The article is saying that Lynch is unlikely to surpass anyone on a depth chart. I believe it's implying that he would not be able to get a starting role. He would be back-up player.