I constantly have issues with Firefox not ending, even though I've closed all of its windows.
Just because you close all open Firefox windows, it does not mean the Firefox is no longer running. Open Task Manager (press Ctrl+Alt+Delete on your keyboard, or press Winkey+R to open a Run... dialog, and type in taskmgr). Click on the Processes tab and press the F key on your keyboard (to quickly locate a process beginning with the letter F). If that process is "firefox", click the End Process button and click Yes at the dialog (if not, click the F key until you find it. If you can't seem to find it, Firefox is probably closed). Attempt to install Adobe Flash Player again.
If you need more help, feel free to send me a message in my profile.
Good luck.
Blake