The ffmpeg from Flathub is a "runtime" package, intended to be used by other flatpak apps. It's not meant for CLI use.
Flatpak apps are not added to your $PATH. They're run with flatpak run appID. Though again, ffmpeg is not an app so it cannot be run this way. Though technically you could use it for CLI use by doing something like flatpak run --command=sh org.mozilla.firefox. This will open a shell inside the flatpak environment, which can use the ffmpeg flatpak runtime.
Though now that I think about it, it would be fun to create my own flatpak package for ffmpeg for CLI use. Should be pretty simple, it would just be a mostly empty package that relies on the ffmpeg-full flatpak runtime. Edit: and I did
The manifest is simply
id: my.custom.ffmpeg
runtime: org.freedesktop.Platform
runtime-version: '24.08'
sdk: org.freedesktop.Sdk
add-extensions:
org.freedesktop.Platform.ffmpeg-full:
directory: lib/ffmpeg
version: '24.08'
add-ld-path: .
command: ffmpeg
modules:
- name: ffmpeg-wrapper
buildsystem: simple
build-commands:
- mkdir -p /app/lib/ffmpeg
- install -Dm755 ffmpeg.sh /app/bin/ffmpeg
sources:
- type: script
dest-filename: ffmpeg.sh
commands:
- /usr/bin/ffmpeg "$@"
finish-args:
- --filesystem=host