Can't disable 'Check spelling while typing' in 'Notes' in OSX El Capitan 10.11.6
Quit all applications.

System Preferences > Keyboard > Text Tab. On the right side you should see "Spelling : Automatic by Language". In drop down list, choose "Set Up..." then uncheck English.

Nightmare free from those red underlines :D

Drawback: doing so will disable Spelling checking in system wide, while you may want to disable in one specific app only.