Flushing a fish down the toilet is not gonna hurt anything including the water because the fish is much cleaner than the poop and pee you're flushing down the toilet.
When you flush the fish down the toilet it goes through your sewer lines and into the street or alley sewer lines and then leads to the sewer treatment plant.
The fish will then likely be scooped out of the sewer treatment plant water and then be thrown in the trash or it may slip through the filters and screens and go back out into the lakes and streams or wherever the water that leaves the sewer treatment plant goes too.
You can also just place the dead fish into the trash can and throw it away or dig a small hole in your yard and bury the fish in a small hole.
But if you want to flush the fish it's not gonna harm anything.