Flushing fish down the toilet is a horrible thing to do. They don't die right away, and suffer massive chemical burns and agony before they do. The only thing it does is remove them from your sight. So please don't flush them.
I am guessing your betta home isn't very big and hasn't had the water changed enough, or regularly enough to keep them clean. That's why they're getting bacterial infections - exposure to their own wastes makes them prone to disease, as well as damaging them in general.
Your fish need clean, larger tanks (preferable separate ones) and regular water changes with a good water conditioner.
At this stage, I would also recommend that they both get an antibiotic treatment. Popeye and fin rot are caused (mostly) by bacteria. So see if you can ask your parents to get some Kanaplex or Furan-2 online, as these are the best medicines for the bacteria that most commonly cause those problems. While you're asking them for stuff, ask whether you can have a new tank or two of at least 1 gallon (it's actually not much more to get two or three gallons...may as well go for broke) and a couple of adjustable heaters (if you don't have heaters already).
This is what is necessary to get your fish back to good health and keep them there.
They definitely need clean, warm water (with 3x weekly water changes) and separate tanks if they're ill. This is absolutely minimal care.
If you think this is too hard/too expensive/your parents won't help -- please do not take the cruel step of flushing your fish. Perhaps somebody here would help you rehome them.
If worst comes to worst, get some clove oil. It puts them to sleep, so they can be put down humanely. But really --- don't be lazy about it, do your best to get treatment/improve their conditions or rehome them, instead of throwing your pets away like garbage.
Last edited by Aus; 08-28-2012 at 03:42 AM.