Here’s exactly what the Flux documentation says about publishing a newly created part to the library:
6- Publishing to the Library
The final step is to publish your part to the library. Publishing is important because new projects in Flux don’t show up in the library by default. You have to intentionally choose to share them there.
Type ⌘P on Mac or Ctrl P on Windows, or
Click on the Flux Menu in the upper left corner of the screen