How to build
It is assumed you've followed the setup guide from https://flatpak.org/setup/
For a one time build, do the following,
flatpak-builder --install-deps-from=flathub --force-clean --repo repo app org.chromium.Chromium.yml
go out to the park and do nice things. It will take hours to build.
If you intend to do development stuff with the package, add the --ccache option and increase ccache size by issuing the following command in the same folder (another terminal tab?):
CCACHE_DIR=.flatpak-builder/ccache/ ccache --max-size=30G
One full build needs about 25G, so more is better.
Credits
Credits go to the brave Chromium packager of ArchLinux. Build instructions are taken from their official package.