I'm no expert but I've heard caustic soda in mildly warm water (not hot water) is a good way of cleaning out a pipe.

Basically you plug it up, some people use potatoes, and then fill it up with the solution of caustic soda.

The more times you do it and the longer you leave it the better the result. For example leaving it for 24 hours then draining and refilling for another 24 hours.

You can probably get more info such as the correct solute/solvent ratio by doing a simple search. I'm not sure how well kerosene will work but I'm sure it would turn out to be more expensive.

You can buy caustic soda at the supermarket, or just use drain cleaner.