Well I can't believe it was this easy. After trying different settings, I found the one that worked. This is for IE 5.5 but if I remember right, it should work for 4.x and above.
Click on tools > Internet options > Security
You will see four choices: 1. Internet 2. Local intranet 3. Trusted sites 4. Restricted sites
Click on Internet. Then in the section that reads "Security level for this zone" click custom Level.
A window should pop up that reads "Security Settings" at the top. The first setting options are "ActiveX controls and plug-ins". Here are the settings I use to disable Flash from downloading and asking me if I want to install it.
Download signed ActiveX controls > Disable Download unsigned ActiveX controls > Disable Initialize and script ActiveX controls not marked as safe > Disable
It was the "Download signed ActiveX controls" that made the difference. I had that set to prompt and Flash would download and ask if I wanted to install it. Doh! Now it don't :)
Now when we go to sites that use Flash and we don't have it installed, we get a pop up telling us that the page might not look right because of our security settings. Just click ok and happy surfing.