How can I clean my dryer vent?
Use fish tape:

It's a sturdy, yet flexible metal rod meant for running cables.  Figure out which of the two openings you can easily pull from, hard.  Insert the tape from that end until it emerges on the other side.  Then cut holes in a towel and secure it to the fish tape with zip ties or hose clamps, and pull it back through.
The rag or towel should force the brush out of its way on the way back.
In the future, NEVER use brush rods that can unscrew to clean a dryer vent.  Only use the kind that are permanently attached to a tough braided wire.