I'm going to flush everything down the toilet in public bathrooms
Why do you want to put everything in the toilets?
Nothing gets really clean in there and when I open the thing it smells like a dead fish
Although disposing of your waste is good, you shouldn't flush random stuff down the toilet. It could clog it.
I'm not flushing things that I don't normally flush.
If I understand you correctly, you are flushing public toilets even before you use them, and then again afterwards?  If so, that may be a bit wasteful, but if it helps with the odor, then you can go ahead.  Just be sure that you are only flushing your own waste and things like toilet paper, as anything else could clog the pipes, at home or in public.