Flash 9 will run on Mac OS X 10.2, which runs on G3 Macs. You can get 10.2 from Ebay or through Amazon reselling. But frankly, don't bother.
I just tried some Flash games on a G3 running 10.3, and performance was so bad they were unplayable. Animations look like slide shows, frame rates are so low and responsiveness so bad you can't control the game.
Not convinced? Many Flash sites won't run on Flash 9, or on browsers that 10.2 runs. Other sites won't even recognize you have it installed, the Club Penguin site says I have to install Flash.
If you want to play games on antique computers, play antique games. 3 In 3, Fool's Errand, and the old Sierra games play great on G3s. If you want to surf the net and play modern games, get a modern machine. Save your sanity and your kids' patience. Even Atom netbooks run Flash better than G3s.