If they're a hard plastic like the ones you linked the only way to flatten them would be with heat - how much heat will depend on the plastic used, and it may not be something you could do with regular home equipment. Not to mention that heating plastic can be extremely toxic and dangerous.
If they're a softer plastic then you may be able to flatten them with a press, possibly some heat. i'd probably cut them in half first. But I'm doubtful you'll be very successful, and they'll likely end up somewhat distorted. I know you want to save them as a memento, but I think making or buying paper bells for your scrapbook would be better.
You might consider a 3-D shadowbox display using the bells and other items from the event.