This doesn't look like a problem with installation, but rather that the installed component is not found by other programs. The installation directory is maybe not in your $PATH.
It's difficult to give hint, without knowing where and how you dealt with install and removing attempts. The Adobe Flash is known to work correctly when running the default installation procedure. AFAIK know the Flash installer is a script, sometimes contained in some RPM or similar package format, but it's not a standard RPM or other package installation procedure. So 'rpm -e' would only remove the installer, if I see this correctly. Maybe your custom removing and re-installation efforts did broke something.