I just finished downloading ClamXav from the App store. I have a separate box dealing with FlashPlayerInstallManager.log! Why is this app trying to install Flash Player on my Mac?
It is not trying to install Flash Player. Since you haven't described exactly what you were doing when you observed this "separate box" I'll guess that you had used either the Open Scan Log or Open Update Log, both of which open the appropriate log file in the Console app and that for whatever reason an old log associated with FlashPlayerInstallManager was already open. You can verify this by checking to see what appliccation is in the foreground indicated by the menu immediately to the left of the Apple menu. If it says Console, then that explains that. The window with the mystery log file should have two columns. The right column contains the contents of the log. There will probably be dates included which will tell you when that took place. The left column should have the name of the log highlighted. If there is no left column, click the button at the top of the window that says "Show Log List."
Flash Player itself is spyware and malware.
No it isn't, it's buggy plug-in software for your web browser from Adobe. You should only download it from http://get.adobe.com/flashplayer/ or allow it to update itself. A new update was just released a day or two ago and Apple blocked the use of any older versions yesterday. There were Trojans disquised as FlashPlayer installers over a year ago, so perhaps that is what you are thinking about.
For faster, more efficient help with ClamXav in the future I recommend you come to the ClamXav Forum.