I want to let my kids play these flash games on my site offline, I would like to have the images and database work just the same as they are online. We have dial-up so it would be nice leave the phone free.
I'd say maybe try Server2Go. Acts like an Apache web server on your local machine. So have backup copy of your site there. That way, 1 - you have backup just in case, 2 - kids can play all day long without using the internet.