Here is my experience with ClickOnce and Packager. I output the package as a C# project so that I could use the "publish" menu item from Visual Studio, a fair shade easier than actually working out how ClickOnce actually works! After I published, I tried the "install" button on the website where I had published it. At that point it told me I needed RedGate.Compression.Zlib.dll in my GAC, so I did that.
Next I clicked Install again, and got the flashing command prompt, same as you.
I then went back into Visual Studio and edited PackageMain.Main() to put a Console.ReadLine right before "return". Now I can see what is in the command window and it says
You don't have sufficient permissions to run an executable located on another machine
My guess is that in all likelyhood it's a matter of adjusting your zone security in the .NET Framework configuration wizard to allow assemblies to run across the Internet. Maybe there is another way around this issue, but at least you can find out what the problem might be.
I hope this helps!