Flushing Kitty litter down the toilet in small amounts is okay as long as your plumbing system is in good working order.
Just don't flush too much kitty litter down the toilet otherwise you could clog it.
You can also just dump the used kitty litter in a garbage bag and throw it in the trash with your normal trash and they will take it.
It's not recommended to flush cat poop with litter because it could cause your toilet or drain pipes to clog especially if you flush too much cat litter down the toilet.
However I've flushed cat litter and cat poop down my toilet for years without a problem.
What I did was remove as much litter from the cat poop as possible and then flush the cat poop and cat litter and then flushed the toilet a few times to make sure the cat litter and cat poop was flushed fully down the toilet.
If you flush too much cat litter along with the cat poop then it could cause a clog but flushing a little bit of cat litter along with the cat poop is okay.