Q: Screen flashes then MBP shuts down.

Hello iansp,

Thanks for using Apple Support Communities.

From your post I understand that your Mac will spontaneously flash the display and then it will shut down.  This indicates there is a kernel panic occuring on the Mac, causing the computer to shut down.  To be honest, troubleshooting a kernel panic can be a tedious and difficult process, so you might want to consider making an appointment at your closest Apple Retail Store, or Apple Authorized Service provider for support.  If you'd like to look at how to troubleshoot a kernel panic, take a look at the link below.

OS X: When your computer spontaneously restarts or displays "Your computer restarted because of a problem." - Apple Support

Take care,

Alex H.