The transitions require the use of Rehan's ShaderTFX add-on. If you've never installed this before, follow the directions on his website and test they work first. If you've already installed a copy of ShaderTFX (registered or unregistered), you can skip these steps.
For a preview of what the flash transition looks like, check out this Blaine's Flash Transitions in Action.
There are two installers depending on whether you are running WMM 6.0 on a 64-bit or 32-bit version of Windows. The installer will put the necessary files into, C:\Program Files\Movie Maker\Shared.
Prerequisite: Rehan's ShaderTFX add-on.
Windows Movie Maker 6.0:
Blaine's Flash Transitions (64-bit) Installer
Blaine's Flash Transitions (32-bit) Installer
After restarting Windows Movie Maker, you should have 3 new transitions with corresponding icons: