Touch the torch again (make sure you touch the same torch you used to spawn him) to receive the Shadow Flames (key item).
If other players in the party also need this key item, they can touch the torch as well - you don't have to fight him for each person.
Head back to Port Jeuno and click on the ??? at the toolbox for a cutscene. This completes the quest.
The Rest
This quest does not need to be active in order to obtain the other (non hand) equipment from coffers. Only requirements for this are that you open them on the appropriate job at the appropriate level of 50+
Guslam mentions something about armor scattered about Vana'diel. You can find two more pieces of armor by simply opening coffers in the following zones:
You must have DRG as your main job when you open these coffers.
Notes
You must have started Chasing Quotas (AF2) before you can start this quest.
If you have any other Borghertz's Hands quest active you will need to complete that one before you can get this quest.
After starting the quest, you can obtain the rewards in any order.
The quest is marked complete upon obtaining the gloves.
The coffer in The Boyahda Tree can be picked by a level 47 Thief using skeleton keys. It took me five attempts to successfully pick the lock this way. Make sure you have a warp method and Perfect Dodge handy in case a fail spawns a Mimic.