I use both Chrome and IE. It appears that each requires a different version of Flash, but can only install one version. How can I get Flash to work with both?
Chrome comes with Flash Player preinstalled; you don't have to worry about that.
Internet Explorer 10 on Windows 8 also comes with Flash Player preinstalled.
All other Internet Explorer versions need to install the Flash Player ActiveX.
Other browsers like Firefox need to install the Flash Player plugin.
What exactly is the problem you are having?