While I've not come across Auchincloss myself, a little searching reveals that his work is certainly a subject of interest in academia, although he may be falling out of fashion to some degree.
There's a very useful resource called JSTOR which collects academic papers, many of which you can read for free if you make an account. Searching for Louis Auchincloss' name specifically reveals 836 results. That's not exhaustive: JSTOR is nowhere near a complete archive and there are likely additional papers that refer to him solely by his last name.
The papers date right up to 2023 but the more recent references tend to refer to Auchincloss tangentially. Focused scholarship on his work seems to have been more popular from the 1970s to the 1990s although I have no solid data for this other than a cursory scroll through the JSTOR search results.
There does not seem to be much commonality in the author's names, suggesting that specialism in Auchincloss is rare. However some of the authors who write directly about Auchincloss are still working: for instance Kieran Dolin at the University of Western Australia.
In terms of a canon, Auchincloss has merited an inclusion in the Encyclopedia Britannica which seems a good place to start:
Notable Works: “Diary of a Yuppie” “Education of Oscar Fairfax” “Her Infinite Variety” “Portrait in Brownstone” “Skinny Island” “Tales of Manhattan” “Tales of Yesteryear” “The House of Five Talents” “The Indifferent Children” “The Rector of Justin” “Three Lives”
The full entry has a more complete list with some additional details.