Is there any difference in cache files for Flatpaked Firefox and the normal one?

I have been using FanFicFare application for downloading Fanfiction stories as EPub from the main fanfiction websites. It works just fine for most of them, but there are now terrible problems with the biggest of them all, https://fanfiction.net, which is behind Cloudflare and generally inaccessible to scripts.

Therefore functionality has been added to script which with appropriate flags (-o use_browser_cache=true -o use_browser_cache_only=true) and when correctly configured it can “download” HTML pages from the Firefox (or Chrome) cache instead and stitch them together into EPub same as if the pages were downloaded from the Internet.

It all works perfectly fine with Firefox as packaged by major distributions (openSUSE in my case), but it doesn't work with Firefox installed from Flatpak. Is there any difference between the storage of cache in Flatpak Firefox? Is there some kind of access protection to its caches?