Cleaning a dryer vent with a sharp elbow
I've had good luck with the brushes that come with the Lint Eater type products you mentioned... but tied on to a piece of rope.

First step is to get the rope through the vent. I hook up a shop vac to one end and feed the rope in from the other. The shop vac will suck the rope through the vent. Sometimes tying a cloth rag to the end of the rope increases the force of the suction on the rope. When the rope arrives at the other end, tie the Lint Eater brush to the rope.

Now comes the fun part: pull the rope back out the other way, dragging the brush behind it.

Additionally, you can tie a rope to the other end of the brush before you pull it back. This lets you pull the brush back and forth a couple of times without having to repeat the shop vac trick.