Does Frankfurt School belong to analytical or to continental philosophical tradition?
It may help to ask the question, what motivated the founding of the Frankfurt School?
- The failure of a Revolution https://libcom.org/files/Failure%20of%20a%20Revolution_%20German%20-%20Sebastian%20Haffner.pdf
Above a very interesting historical account by Sebastian Haffner
- And the work of a gentleman by the name of Dr. Sigmund Freud, and I can highly recommend a very careful reading of Freud’s masterpiece https://www.stephenhicks.org/wp-content/uploads/2015/10/FreudS-CIVILIZATION-AND-ITS-DISCONTENTS-text-final.pdf
Then you will be well prepared to study the work of the Frankfurt School in my opinion
PS To be more explicit, the Frankfurt School was trying to answer the question (at least at the beginning) of this: since all signs pointed to a socialist (let’s say Marxist) revolution in Germany, why then did the revolution fail?
We have to remember the psychiatrist Erich Fromm was brought into the Frankfurt School for a reason. He was a psychoanalyst. Later on Herbert Marcuse carried the torch of Freud for the School. His “Eros and Civilization” https://gonzaga.academia.edu/JoanBraune
It is interesting to note that Freud himself was analytic. One undergoes “analysis”. Though the word is used by Freud in a slightly different context.