Please try the offline installers. Links are at the bottom of the guide. Also, it would be great if you could share your installation logs, so that I can pass those along.
Flash Player *is* a built-in component on Windows 8 and higher, and is managed through Windows Update. I'm not sure why we're detecting Win7 incorrectly in this instance, but the logs should help us identify and correct it, if the issue is on our side. This isn't a widespread problem based on what I see in the aggregate installation traffic, but we definitely want to investigate it.