Its not the Linux distro, its the browser. Adobe stopped releasing Linux plugins for FF etc at V11.2. Newer flash stuff needs a later plugin but the only way I know of on Linux to do this is to
either install Chrome, which comes with Flash Player and gets updates,
or find a way to install the
pepper flash plugin that Chrome uses.
Ubuntu has a ppa for the pepper flash plugin, which is why I'm running Chromium, and presumably why Lidl's online leaflet works for me.
Details on the ppa and the needed files can be found
here. As its Ubuntu, and thats based off Debian, I would imagine a little bit of tinkering should see it working on Debian also. Arch Linux also has pepper flash available. Fedora I have no clue about !!