Randomly oriented fossils may indicate an autochthonous deposit whereas parallelly oriented fossils indicate directionality of flow. How?
Lots of bones are long and thin and fairly heavy, to turn them all in the same direction water flow has to be fairly fast, we see the same thing today. fast flowing water turns bones and logs to present the least drag. This is important because it was one of the first ways used to establish bones whether had been moved by the environment after death.
John is totally right. I just want to add one more information: most fossils have one side or end, which is heavier than the other (for example look at belemnites). The heavy end will point to the direction the current comes from. The lighter end will freely orient in the direction the current goes to. Paleontologists call this anchored deposition.
Autochthonous deposits are autochthonous, because they show no signs of transportation.
You shouldn't differentiate between "current and autochthonous", but between autochthonous and allochthonous. Latter indicates transportation of the fossil away from its original deposition place. Even this transportation might me chaotic and not perfectly oriented in one direction, depending on the flow rate and the fact what flows there (water, debris).