Although trained as an entomologist, and a specialist in dragonflies and orthopterans, Flower began studying paleontology in the middle of the 1930s.
He became an expert in North American cephalopods of the Devonian period as well as the stratigraphy of the early Paleozoic era.
His main field was the nautiloids, which he studied intensely, often focusing on life habits and theoretical aspects of paleobiology, but he also penned many papers on fossil corals and other invertebrates.
In the paleontology community, Flower's colorful behavior earned him admirers and enemies—whom he would occasionally "thank" in the acknowledgement sections of his papers or, in one case, in the name of a fossil species.
His antics included mocking the alleged low-standards of one organization for paleontologists by dressing as an ape for a conference, and by having his dog inducted into the society.