I had success recently at using CO miles for an Emirates award from VIE-BKK return. The process is as SeattleBH describes earlier, but I had pretty good luck just picking flights that showed good availability using the KVS tool. In every case, if Emirates did not immediately (within seconds) deny the reward, it wound up being confirmed at the 24 hour mark.

Sorry but I have no insight into the JFK-HAM routing.