Google embeds Flash Player in Chrome. Unless you're having issues with the embedded version you shouldn't have to download Flash Player for Chrome. For IE, launch IE and go to Adobe - Adobe Shockwave Player and download the installer. The download page detects the OS and browser and offers the appropriate plugin for the OS/browser combination so you'll need to use IE to download the correct Flash Player for IE.
Flash Player and Shockwave Player are two different plugin types and are not interchangeable. The vast majority of users just need Flash Player for viewing Flash content on the web. If you need to install Shockwave Player (e.g. to view content authored using Adobe Director) then you should also install Shockwave Player. To install Shockwave Player, go to Adobe - Adobe Shockwave Player and download the installer. If you don't view content authored in Adobe Director then there is no need to install Shockwave Player.