I have struck this problem many times and it has sent me insane Luckily my hair is already grey.
Here are the steps I now use with 100% success.(12 times out of 12)
Search the registry(CTRL F) for flash (put a space after the word flash)
The first key it finds, try and delete and you will find it does not allow you to.
Which is why the install fails because it cant overwrite the key.
Right click the key and click on permissions.
Select either the everyone logon or domain users if you are on a network and give them full permisions. Click advanced select the box for replace permission entries and apply.
You should now be able to delete the key.
Press F3 to search again and repeat the above for the second key found.
Flash will now install.