The ending resolves the Dolarhyde case in Florida and then hands the story to The Silence of the Lambs (1991) in a single exchange. Dolarhyde fakes his death, tracks down the Graham family and holds Josh at gunpoint. Graham and Dolarhyde injure each other in a brutal fight, and Molly shoots Dolarhyde dead.
Afterward, Graham receives a note from Lecter, who remains imprisoned. In the final scene, Dr. Chilton tells Lecter that a young FBI trainee has come to see him, and that line leads straight into the next film in story order.
Why does Dolarhyde fake his death before the finale? In my opinion, it is the film's smartest structural move. Reba is believed lost, Graham is led to think the case is closed, and the family in Florida is left exposed, so the last act turns from a procedural into a home invasion. Graham has spent the whole film studying the killer through film processing records and Lecter's cryptic hints, and the payoff arrives where he feels safest. It could be argued that the people who finish the job are the ones with the most to lose: Molly fires the shot, not the profiler, which pays off the family the film spends its first act setting up.
How does the ending compare with the earlier adaptation? Manhunter 1986, directed by Michael Mann, covers the same Thomas Harris story with William L. Petersen, Tom Noonan and Brian Cox. Red Dragon (2002) earned about $209 million on a $78 million budget, according to Box Office Mojo, and Brett Ratner closes on Lecter rather than on the Graham family. In my opinion, that is a choice about what the audience came to see, and a reasonable one for a film released after two Anthony Hopkins hits.
The Chilton scene is also a continuity device. Anthony Heald plays Dr. Chilton here and in The Silence of the Lambs, and Frankie Faison plays Barney in both, so the asylum staff are the same faces when the trainee arrives. Perhaps the Chilton line is a little neat, but it gives anyone watching in story order a clean bridge into 1991. The handoff works best when you watch Red Dragon directly before The Silence of the Lambs.
So, to answer the common question: yes, the ending is built to connect to The Silence of the Lambs.