Please note that this is not an official Flatpak release of Cromite.
Cromite's developer uazo is looking into making an official one.
First, you need to install flatpak-builder on your system.
It should be available as a package on your Linux distribution.
All of the following commands should be run as a regular user (not root).
flatpak install org.chromium.Chromium.BaseApp/x86_64/23.08
git clone https://github.com/syhlx/cromite-flatpak.git
cd cromite-flatpak
flatpak-builder --user --install --force-clean build-dir org.cromite.cromite.yaml