Although VS Code is a great editor for TypeScript projects, it needs a kick every now and again. Often, without warning, certain files cause it to freak out and complain. Mostly the fix seems to be to save and close all open files, then open tsconfig.json. After that you should be able to re-open the offending file without error. If it doesn't work, lather, rinse, and repeat.
If your tsconfig.json specifies its source files using the files array, IntelliSense will only function correctly if the file in question is referenced such that VS Code can find it by traversing the input file tree.
Edit: The 'reload window' command (added ages ago now) should solve this problem once and for all.
~ Answered on 2016-07-10 21:39:46