Photos reproduced under CC: top - copyright lynx81, bottom - copyright johnbullas both Flickr
I for one have never heard of the idea of flushing cat litter down the toilet. It seems though that some people do it. I would have thought that you risk blocking the drain with the "litter element" of the cat litter. Anyway, there are hidden dangers in respect of health as well.
In London pet owners, usually dog owners, who take their dogs for a walk in the park are requested to pick up their dog's droppings from the grass to avoid the potential for passing on disease such as Toxoplasmosis.
The same kind of potential health risk exists for wildlife if you dispose of used cat litter down the toilet and this I presume must include toilet trained cats (i.e. cats who use the toilet like humans).
Some cat feces (feaces in the UK) contain a parasite called Toxoplasma gondii. This parasite is in wildlife such as rodents. When cats catch rodents and eat them they ingest the parasite and is then expelled with the cat's feaces.
Sewage systems can't remove the parasite so it is carried into the sea with the treated sewage. The parasite is then ingested by small sea creatures which are in turn eaten by such beautiful creatures such as the sea otter. The parasite can kill animals and seriously harm humans.
Lesson: throw cat litter into the refuse, double wrapped, where it will be placed in land fill and the parasite will die. (land fill is another problem however; we are running out of land fill space in the UK).
Normally cats would go to the toilet outside on soil and bury it. The parasite would die after one year. It is the artificiality of modern living with humans that seems to be the cause of this problem.
One solution put forward is to keep cats indoors to prevent them catching and eating wildlife but does that sound correct?
Do you flush cat litter down the toilet? Read this. to Cat litter and burying feces