The story was written in 1931 and is about an antarctic expedition in the same timeframe. In the story the planes were brought disassembled by ship and were reassembled in the antarctic. This is the author's description:
Four large Dornier aëroplanes, designed especially for the tremendous altitude flying necessary on the antarctic plateau and with added fuel-warming and quick-starting devices worked out by Pabodie, could transport our entire expedition from a base at the edge of the great ice barrier to various suitable inland points, and from these points a sufficient quota of dogs would serve us.
The 1920s saw several aerial expeditions to both the Arctic and Antarctic by aviators such as Hubert Wilkins and Richard E. Byrd (who flew over the South Pole in 1929, having (possibly) flown over the North Pole in 1926). The most direct inspiration for the specific model, though, seems likely to be Roald Amundsen's 1925 attempt to fly the North Pole, as that was made using Dornier Do J Wal (Whale) flying boats (Byrd and Wilkins flew various types, but not Dorniers).
Amundsen was unsuccessful; his two aircraft were iced in after landing, one was damaged, and it took several weeks to free the other to take off with all members of the expedition aboard. It was front page news at the time, so seems a good candidate to inspire fictional expeditions. The Dornier that did make it back was in the news again closer to the time of writing as Wolfgang von Gronau made a transatlantic crossing in it, which may have been an additional reminder.
[Edit: after doing a bit of digging, /u/kingconani provided a better answer a couple of years back, with some more detail; should've searched harder to start with!]