You can unlock FL Studio and all other products you own from demo by using FL Studio's Help > About Dialog. The procedure below requires you have an Image-Line account containing FL Studio, as the program will sign in to your account and downoad and install an unlock-key automatically.
This procedure updates your FL Studio regkey from your Image-Line account. This can be used to unlock FL Studio from demo for the first time or after purchasing new plugins or after updating/upgrading FL Studio.
After restarting, the Help > About Box will show your name and registration number along the top of the box
Unlock Windows VST Plugins & Content - see 'How do I unlock my software with the registration file?'
Unlock Mac OS X VST Plugins & Content - see 'How do I unlock Mac OS X VST plugins?'
Activate Boxed software - see 'How to register your Boxed software'
How do I get an account? - See here for details on how to set up an Image-Line Account.