I don't really agree with flushing because it isn't really an instant death. I have never really had to deal with this issue...but when my fish in the past have become ill I do attempt to treat (mediate) them and if the treating doesn't work they are usually dead the next morning. I have never had a fish linger...
I did overdose my sick fish once and it was a pretty quick death but it wasn't intentional. I have heard of the method where you put your fish to sleep using clove oil and then add vodka (which kills them).
This website has a list of euthanasia methods:
How to Humanly Euthanize Your Fish - Rate My Fish Tank
most people frown on flushing. most put them in the freezer wich I think is just as cruel cause then the fish freeze to death. I'm more of a quick kill person. now mind u I have no emotional attachment to my fish so it's simple for me to kill them. but a sudden impact to the head works for me. for a large fish, say and oscar laying it on the ground and pop it with a hard object and thats good enough to finish it off. pretty much destroy the brain as quick as possible. thats y with the catfish I bring home from fishing I hit in the head with a board with 3 nails in it. nails penatrate the brain and the fish dies painlessly. I would tell u how I finish off my cichlids when they have problems but I would get strung up here I think.
That is slightly graphic...but I agree with the quick death idea. Maybe not your methods because I usually develop an emotional attachment to my fish, but to each his/her own.