In "A Leak in the Fountain of Youth", Amelia Reynolds Long follows an old tradition common to science fiction in particular and to fiction in general. When works of prose fiction were a recent invention in the late 17th and early 18th century, writers such as Aphra Behn, Daniel Defoe, and Jonathan Swift would ease their readers into their fictional worlds by writing in the first person, and having their narrators explain how they came to set their experiences down in writing. Later, in the late 19th and early 20th century, when science fiction was a new genre, the same thing happened: writers would ease their readers into their worlds by writing in the first person, such as the unnamed narrators of H. G. Wells' The Time Machine and The War of the Worlds, or John Carter, the narrator of Edgar Rice Burroughs' early Barsoom novels. Long follows this tradition by having Eric Dale, the narrator of "A Leak in the Fountain of Youth", explain to the reader why he has chosen to publish an account of the doings of his friend Professor O'Flannigan.
Long also sets out to produce a humorous story, which has always been relatively rare in science fiction. Mind you, the story's humor is broad even by 1930s standards: the reliance on Irish surnames (especially McGillicuddy) as intrinsically funny, and the poet-as-esthete stereotype (first popularized by Oscar Wilde in the 19th century).
As for the story's science content, it's mostly a handwave to allow for the story gimmick, a serum to reverse the aging process. The functions Long assigns to the various glands are largely erroneous, and I have been unable to find any mention of separate amoebas joining together to form a single individual.
Long wrote a second story featuring Professor O'Flannigan, "Reverse Phylogeny", which will also be appearing in this blog. It seems reasonable to assume that Long intended to write a whole series of "Professor O'Flannigan" stories, but by the end of the 1930s she had become unhappy with the direction science fiction was taking, and turned to writing mystery novels instead.