The dragon armour is potentially one of the best sets of armour in the game, though except for the experience and level of Elemental Strike (IIRC) gained when you have completed the set, there is no great need for it.
Sometimes Sir Patrick is just stubborn, and talking to the dwarven king, Grisha and Patrick repeatedly will trigger the speech option. If that doesn't help, there is a workaround, described in a reply to;
FIX for broken Imp Council Member quest 
