Is there any difference in meaning between the adjectives Kafkaesque and Kafkan, or are they synonyms?
Of or relating to Franz Kafka or his writings.
Marked by surreal distortion and often a sense of impending danger: "Kafkaesque fantasies of the impassive interrogation, the false trial, the confiscated passport . . . haunt his innocence" (New Yorker).
The adjective kafkan, though used, is not easily found in dictionaries.
I think that kafkan is more used in the meaning n. 2 of the above definitions.
The first Google Books search result for either Kafkan or Kafkaesque involves an author struggling with this very question of how to make a suitable adjective form of Kafka. From The New Yorker, volume 14 (1938) [combined snippets]:
...very Franz Kafka-ish (Kafkan? What is the adjective?), called "The Wild Goose Chase," which I seem to have recommended with some warmth. Looking back on it now, I feel that it was more confused than original, my primary reaction having been vice versa. Of those whom my ill-considered praise may have led to a bewildered stab at Mr. Warner's cryptic allegory, I crave pardon.
The earliest Google Books Match for Kafkaesque is from eleven years later, in 1949.
Google Books actually finds a sufficient number of matches to track Kafkaesque (red line), Kafkan (blue line), and Kafkaish (green line), thought he green line looks pretty flat in this Ngram chart for the years 1935–2005:
Today the clearly preferred form is Kafkaesque, a point underscored by the fact that Merriam-Webster's Eleventh Collegiate Dictionary (2003) has an entry for Kafkaesque (which it dates to 1946) but no mention Kafkan or Kafkaish as variants. Incidentally, the Eleventh Collegiate has only one definition for Kafkaesque, unlike the dictionary that Josh61 cites in his answer:
Kafkaesque adj (1946) : of, relating to, or suggestive of Franz Kafka or his writings; esp : having a nightmarishly complex, bizarre, or illogical quality.
In my opinion all three of the words discussed here are recognizable adjective forms of Kafka, but I don't think that they have substantively different meanings, and I don't see any reason in general to stray from using the most familiar form, Kafkaesque.
Kafkan: (a person or character) of a type epitomised by Kafka or one of his characters.
kafkaesque: (a situation, problem, or plot) recalling the nightmarish situations described in Kafka's stories.