On Windows XP SP3, the Flash Player install (just done now) also added Google Toolbar without asking. When trying to remove it in Control Panel, the OS says the application can't be found. I'll try rebooting to see if this is the case, but right now it's showing up in the browser so it must be installed and the behavior may be an artifact of a fresh install.
Multiple dialogs appear during the Flash update. It is possible that one of the "Run" dialogs for the activex control or other executables hides the dialog for choosing the toolbar. Regardless, the install process must be made cleaner so this does not happen. Google is well known for collecting unauthorized data from users. Adobe should not be participating in this kind of snoopery.
All I can do is give you the download links for the offline installers, which are not bundled with any 3rd-party software: http://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html#mai n-pars_text_4
Update: After rebooting, I was able to successfully remove the toolbar in Control Panel.