On an archlinux system, I noticed the ability to right click the
firefox desktop entry, and have both "new window" and "new incognito
window."  This appears to be achieved in their .desktop file:

https://github.com/archlinux/svntogit-packages/blob/packages/firefox/trunk/firefox.desktop

On Debian, launching an incognito window requires the extra step of
first launching a firefox instance, and using the GUI to spawn a
second window.  The arch solution is nice, as it allows a simple right
click action.

https://specifications.freedesktop.org/desktop-entry-spec/desktop-entry-spec-latest.html#extra-actions-identifier