How can I export a PDF from GIMP with each layer on a new page?

GIMP (prior to 2.10) can't do this directly.

You need to use an intermediate file format.

Prerequisites

sudo apt-get install imagemagick

Steps

1. Export from GIMP as an MNG animation: File → Export → document.mng

2. Convert to PDF on the terminal:

   convert -reverse document.mng document.pdf
   

Gimp (2.10) does it already. No extra software or plugins needed.

1. Import all images/pages as layers.
2. File > Export As > filename.pdf
3. Select Layers as pages and Reverse the pages order
4. Click the Export button.

That's all! Enjoy.

There is a Gimp plugin that does this nicely.

http://registry.gimp.org/node/27987

The install path and how to change the permissions are covered in this blog post: https://www.zyxware.com/articles/4438/how-to-export-multiple-layers-from-gimp-into-a-pdf-file