Go to a music store a buy a trombone snake - depending on how big your tubing diameter is. If you are under 5/8" ID you should be OK. It should cost under $10.
This style is nice because you can push and pull it through the tubing. You can also find a brush the right diameter, cut the handle off and tie a piece of good string to each end. Put a weight of some kind on one string end so you can drop it through the tubing. Then just pull the brush through.