I want to write my application using flux architecture, but I want to do this without any external libraries, npm, etc. Is this possible?
Yes, indeed it's possible
You could either:
Write your own flux implementation, it's really quite simple.
OR - if it's the idea of referencing external NPM packages that you don't like, just download the package once only and then copy the code into your source code so that you're not relying on NPM.