Paddle upstream before you start fishing or stash a bike at the takeout and pedal back to car (leaving kayak at takeout).
No chute or driftsock, you are moving along pretty much at the same speed.
A drag chain is ok, but if it snags (and it will eventually) you are in for a sudden jerk. With the low freeboard of a kayak, it is very easy to end up in the water. I prefer finding places to wade (and using the kayak for shuttle) or using an anchor off the bow (only in calm water, otherwise it is like snagging a chain above).