Proto-Indo-European *(s)lei- "slimy, to glide" in an extended form became Old English slīm then slime.
In the suffixed form *lei-w- it became Latin oblīvīscor "to forget" (with the prefix ob from PIE *epi- "near"), the etymological sense being "to wipe, let slip from the mind" (AHD). This became French oublier "to forget" and oubliette - I guess because when you put someone in an oubliette, you can forget about them.
Some disagreement here, however: Lewis & Short state that oblīviscor "to forget" is from ob plus livēre "to become dark". The ODEE says "of obscure origin" for oblīviscor.
flummery, which originally referred to a kind of porridge, is from Welsh llymru "soft jelly from sour oatmeal." (The Welsh voiceless lateral fricative /ɬ/ can sound like /fl/ to English ears.) llymru is from llym "sharp, severe, pungent." This is perhaps derived from *(s)lei-. Pokorny has "perhaps Welsh llym 'sharp'" in the entry for 3. lei 662. The etymological lexicon of Proto-Celtic says Proto-Celtic *lim- "sharpen, polish" is probably from *(s)lei-.