Why can I download the latest Adobe Flash but not install it?

The error message is always the same: “The Adobe Flash Player is required for video playback. Get the latest Flash Player.”

I have Mac OS 10.7.4 and both Safari 6. and an up-to-date Firefox. When I download the latest Adobe Flash, which is free, I am supposed to first click on the window where I agree to the terms. That never appears; nor does the install icon.

Any thoughts? I hope to avoid a sweaty call to Apple support, if possible.