Question: The proposition "from" is could be used to indicate the source. In this example (context is soccer, or association football): 

> 
> [link](http://en.wikipedia.org/wiki/Argentina_v_England_(1986_FIFA_World_Cup)#Lineker.27s_goal_and_Argentine_victory)  
> 
>  "England were unable to score an equaliser - Olarticoechea making a particularly important defensive contribution in the 87th minute when he and Lineker both jumped for the ball ***from*** another Barnes cross, the two players collided, both missed the ball by a whisker..."
> 
> 
> 

A ball is a physical object. A cross is the act of sending a ball across the field. The part: 

> 
> "...when he and Lineker both jumped for the ball ***from*** another Barnes cross..." 
> 
> 
> 

suggests that a physical object (ball) could somehow appear as a result of an act (cross), which sounds weird. An abstract version of "*the ball from a cross*" would be "***[an object]*** from ***[an action]***", which suggests that the "*[action]*" has a hand in creating the "*[object]*".

Would this: 

> 
> "...he and Lineker both jumped for the ball ***on*** another Barnes cross...." 
> 
> 
> 

be possibily better?

Answer: 
I agree with your parsing of (*he and Lineker) (jumped (for (the ball (from another cross))))*
as opposed to the alternate given by @Jay of *(he and Lineker) (jumped (for (the ball)) (from another cross))*. The natural assumption is that the ball came from the cross, not that the players came from the cross; especially since a *cross* is, as you say, an action performed on a ball.

However, I see no reason why the idea that a ball appears somewhere as the result of a cross should be weird; the whole point of a cross is to make the ball disappear from location A and appear at location B on the opposite side of the field.

So it doesn't seem odd at all to me, in fact it sounds perfectly reasonable and natural.
I take it this is from the description of a football (soccer) game? Sorry, I'm not familiar with the terminology of the sport. But assuming that, as you say, a "cross" is an action ...

The quote does not say that the ball came from a cross. It says that they jumped from a cross. "For the ball" is a prepositional phrase acting as an adverb to modify "jumped". Eliminating some modifiers, you could simplify this sentence down to "[The two men] jumped from a cross." So they did a cross, and then from that cross they jumped.

The difficulty that often arises is that the same construction could have a totally different meaning. In a different context, you could say, "They asked for the ball from Sweden", meaning, they asked for the ball, and the ball is from Sweden.