(set in 1923?, written in 1923, published in 1924)
We had devised two weapons to fight it; a large and specially fitted Crookes tube operated by powerful storage batteries and provided with peculiar screens and reflectors, in case it proved intangible and opposable only by vigorously destructive ether radiations, and a pair of military flame-throwers of the sort used in the world-war, in case it proved partly material and susceptible of mechanical destruction ‒ for like the superstitious Exeter rustics, we were prepared to burn the thing’s heart out if heart existed to burn.
The US military did not have flamethrowers during World War I except for a few samples of the French Schilt No.3 (Investigator Weapons 1: The 1920s and 1930s, p. 106). Most of these remained in Europe when the war was over. This makes it highly likely that the surplus flamethrowers obtained by Dr Elihu Whipple and his nephew were former German weapons brought to America as war trophies. The returning US troops brought back huge amounts of captured weaponry, including machine guns and other heavy weapons. Flamethrowers were completely unregulated at the time (Investigator Weapons 1, p. 20).
That the mentioned flamethrowers were of German design is indeed likely since the Germans invented this type of weapon prior to the war and used it probably more extensively than the British, French, and Italians, who all eventually designed their own patterns.
The Whipples had acquired two, which indicates that they were of the smaller, man-portable type. The Germans introduced several man-portable designs during the war, including the Fiedler Kleinflammenwerfer Modell 1912 and Modell 1917 (“small flamethrower model 1912 and model 1917”) or Kleif.12 and Kleif.17, and the HAG Wechselapparat Modell 1917 (“interchangeable device model 1917”) or Wex.17. Notably, these were not actually issued as one-man weapons, but operated by a pair of combat engineers, one carrying the fuel tank, the other aiming the nozzle. However, they could be used by a single person, especially the fairly advanced Wex.17.
The place to go to buy military trophies in the 1920s would be Francis Bannerman Sons of New York (Investigator Weapons 1, p. 25). Their mail-order catalogue from 1925 does not list flamethrowers, but that does not mean they did not have any. Of course, the Whipple nephew might be a veteran and could have brought back the things himself.