I also don't get flash player to work in chromium.
My configuration:
LibreElec Version 7.0.3
Architecture Generic X86_64
I recently upgraded from openElec (where flashplayer in chromium was working).
after upgrade chromium was still available and I believe auto upgraded, but flashplayer no longer worked.
I have tried installing libpepflashplayer.so from chromium configuration, action tab. installation succeeded was reported.
I also tried uninstalling chromium, reinstalling chromium and again installing the pepflashplayer. This didn't work as well, however after this action still all my bookmarks were in place in chromium so I doubt the uninstall was very thorough.
Suggestions? Let me know if I could provide additional info.