Flathub is the central place for installing, building and hosting Flatpak builds. Blackbody is available after registering the repository from its Flathub page. Also check out Blackbody's project site.
To install Blackbody hosted on Flathub, use the following:
flatpak remote-add flathub https://flathub.org/repo/flathub.flatpakrepo
flatpak install flathub eu.nimmerfort.blackbody