The Flaming Deeps are mostly unexplored, but the dwarves do know that there are strange Orcs inhabiting the Deeps.
Defeat 18 Ghash-hai Orcs
Talk to Hysing at Anazarmekhem
Hysing is at Anazârmekhem at the north end of the Flaming Deeps.
Hysing will be interested in hearing more about what you encountered while battling the Ghâsh-hai.