I joined just to respond to this.
What I did:
Make sure you have Flash installed already
Install 7-zip or winrar if you don't have it already
Download the LDD installer from Lego
Download the Flash installer from Adobe
Extract the LDD installer file (i.e. setupldd-pc-4_3_11.exe) (Extract to "setupldd-pc-4_3_11\")
Drag the Flash installer into the setupldd-pc-4_3_11 folder
Navigate into the setupldd-pc-4_3_11 folder
Copy the name of the included (was packaged with the LDD installer) flash installer, then rename it (I added "_0" to the file name) - Could probably just delete the file, really
Rename the downloaded flash installer with the name you copied from the pre-packaged one
Double click LDDSetup.exe
When it asks to install Flash, click yes
What I found was that the newly downloaded installer was used, and I was told I was either installing an old version of Flash or already had flash installed, and was given the option to download a newer installer from Adobe (maybe I downloaded an old installer?). I clicked through to download from Adobe, and the LDD installer continued as though the Flash installation was successful. The file associations seem to have worked as a result of this.