The installer will automatically install both 32-bit and 64-bit players on a 64-bit system. You can check it
- 64-bit: C:\Windows\system32\Macromed\Flash
- 32-bit: C:\Windows\syswow64\Macromed\Flash
What browser are you using? As Pat says, we have a monolithic installer that includes both the 32 and 64-bit versions of the NPAPI plug-in on Windows. Your browser will automatically choose the appropriate version. As an example, Firefox is a 32-bit browser, so it will choose the 32-bit NPAPI plug-in regardless of whether the underlying operating system is 32-bit or 64-bit. Google Chrome 37+ will include a 64-bit browser when a 64-bit operating system is present, and a matching 64-bit Flash Player will already be included, requiring no additional download.
I've included screenshots of both the Add-In Info from Internet Explorer 11 on my Win7 x64 machine, as well as a screenshot of Task Manager, showing the Flash Player process running in 64-bit mode. The *32 next to various process name denotes the 32-bit processes running at the time. The filename FlashUtil64 denotes the 64-bit process as well.
While I think that this should be the case by default, you may want to confirm that 64-bit processes are enabled in EPM mode on Win8+: