Hey I had the same problem and tracked down a solution. Maybe not all these steps are necessary, but this got the job done for me:
First close all of the Browsers in your Dock by holding down the mouse on the icon and then clicking quit.
Then click Command-Space Bar to show the Spotlight field.
Type the words Activity Monitor in the Spotlight field.
A window will appear showing you all of the activities running on your computer.
Try to click on Dashboard Client (in the Process Name column), and then click the stop sign image that says Quit Process.
Somehow that didn't work for me, though, so then I clicked on Dock (in the Process Name column) and then I clicked the Quit Process stop sign, and it successfully quit the Dashboard Client (which is part of the Dock I think).
Then click again on the Install Flash Player icon on your desktop. It should work after a try or two (it almost worked for me, then said there was an error, but I clicked on the Install Flash Player icon yet again and it finally installed properly, and I can use Flash Player now). Good luck!