Thanks for posting about this! I never thought to try this as an Akregator user, but it's a great idea... I spent the past day getting this to work since I also use the Flatpaks; hope it helps.

As suggested by @progandy@feddit.de, one solution is to define a custom protocol where the URL gets passed to a script that opens Firefox Reader with the URL; here's what I've done:

1. Decide on a protocol name, which the URL will be prefixed with and passed to xdg-open since that should be available to the Flatpak. I used firefox-reader as the protocol, so I put xdg-open firefox-reader://%u as the custom command (so a command Akregator would run might look like xdg-open firefox-reader://https://example.com).
2. Define a desktop entry to support the custom protocol (you can see mine below). ~/.local/share/applications is the standard place to put these, as far as I'm aware. Since the custom protocol needs to be removed from the URL, I wrote a script (also below) to do this and then call Firefox with about:reader?url= prefixed. The script can be anywhere in $PATH.
3. Add the desktop entry as a "default application" for opening URLs using this custom protocol. In my case, I ran xdg-mime default org.mozilla.firefox.reader.desktop x-scheme-handler/firefox-reader (org.mozilla.firefox.reader.desktop is the name of my desktop entry file).
4. You also might have to update some mime/xdg database stuff. I had to run update-desktop-database ~/.local/share/applications so xdg-open would find the "Firefox Reader" desktop entry.

[Desktop Entry]
Type=Application
Name=Firefox Reader
Exec=open-firefox-reader.sh %u
StartupNotify=false
MimeType=x-scheme-handler/firefox-reader;

#!/usr/bin/env bash

flatpak run --user org.mozilla.firefox about:reader?url="${1#firefox-reader://}"

If you have any other trouble or want to find more information about this since the desktop entry could probably be tweaked, here are the sources of note I used to figure this out (If I forgot a step or two writing this, they should also be present somewhere in there):

• https://unix.stackexchange.com/questions/497146/create-a-custom-url-protocol-handler
• https://wiki.archlinux.org/title/XDG_MIME_Applications
• https://wiki.archlinux.org/title/Desktop_entries#Update_database_of_desktop_entries

Maybe you can register a custom protocol and have your own script outside of flatpak that runs firefox. Then use an xdg-open command that prefixes the custom protocol.

This is 100% a firefox question, you may want to rephrase it and ask in a firefox forum.