Character Analysis
As with those of other family members, friends, and colleagues, appearances by Wilhelm Fliess in The Interpretation of Dreams tend to say more about Freud's personality and perceptions than they do about Fliess himself.
Fliess was a physician in Berlin who specialized in matters relating to the ear, nose, and throat. Freud and Fliess had an intense but in some ways ambivalent friendship (they were kind of frenemies), and that combination of intensity and ambivalence tends to come out in Freud's dreams—even if Freud doesn't always admit that himself.
For instance, Freud's iffy feelings for Fliess "served as additional background material" in the Dream of Irma's Injection (source). In 1895, Fliess had operated on one of Freud's patients, and a serious surgical error endangered the patient's life (source). Freud's conflicted feelings included guilt for his own role in the incident (he had referred the patient to Fliess), feelings of blame for himself and for Fliess, and, on top of that, a strong desire to exonerate both Fliess and himself from any guilt or wrongdoing (source).
Late in The Interpretation of Dreams, Freud says this to his readers: "My emotional life has always insisted that I should have an intimate friend and a hated enemy. I have always been able to provide myself afresh with both, and it has not infrequently happened that the ideal situation of childhood has been so completely reproduced that friend and enemy have come together in a single individual—though not, of course, both at once or with constant oscillations, as may have been the case in my early childhood" (6.9.50).
Freud's friendship with Fliess fit this pattern perfectly (source). For many years, Fliess served as the "intimate friend" to whom Freud turned for validation and support. As Freud reflects to himself at one point in the book:
What a number of valued friends I have lost, some through death, some through a breach of our friendship! How fortunate that I have found a substitute for them and that I have gained one who means more to me than ever the others could, and that, at a time of life when new friendships cannot easily be formed, I shall never lose his! (6.9.55)
Unfortunately (or maybe not?), Freud did lose Fliess's friendship around 1902 (source). With that in mind, it's possible to see that the later editions of The Interpretation of Dreams aren't just scientific treatises or kinda-sorta autobiographies; they're also chronicles of a friendship that went down the tubes.