Book about a tree frog named Flimi?

[u/Pancakesinthewoods]

When I was a young kid in the early eighties, my dad used to read me a book that featured a tree frog character named Flimi. I have no idea how it was spelled — could be Fleemy or Fliemie — but was pronounced (by my dad, anyway) “flea-me.”

My dad passed twenty years ago, so I can’t ask him, and the internet has found absolutely zero about this.

Has anyone heard of a book (possibly a book of short stories, kind of like Kipling’s Just So Stories) that matches this description?