What you can do is that you follow Rashad, the man who is treating Duke Eltan when he leaves the Flaming Fist headquarter in the evening and see where that will end.
Or you can immediately enter the headquarters and kill anyone between the party and Duke Eltan. Alternatively, sneak in with a strong thief or someone strong and invisible. If you are hiding or invisible, you can avoid a fight with the enemy upstairs too. When you reach the second floor where Duke Eltan normally is, you find him and the man treating him, Radesh, who after a conversation turns out to be a greater doppelganger trying to kill the party. After he is killed, Duke Eltan will ask of you to bring him to the Harbormaster, who is good friend of Eltan and can hide him from the loyal followers of Sarevok until he is recovered.
When Eltan is brought to the Harbormaster, the Harbormaster will hide him and promises to take care of him. The party gains as a reward 2500 experience points and has probably done something good for the future of the city.