Dragonite always seemed so odd to me. In so many ways, he seems like a parody of the traditional European dragon...he's fat, his wings are ridiculously tiny, he has no teeth or claws to speak of, he rescues people instead of eating them, etc. Then in Gen 3, Gamefreak created Salamence, your standard mean-looking dragon. Doesn't it seem like they should have done Salamence first?
Anyway, that's a cool idea. Dragon/Fighting would go with the concept of Dragonite being a "knight" (at least, that's how I always saw his name), turn a crippling SR weakness into a resistance, and differentiate him from Salamence. Trouble is, it might make him a little too good...I don't think anything resists both Dragon and Fighting, since the only type that resists Dragon is Steel. STAB Close Combats coming off 134 base Attack is not a fun prospect. That type combo would be cool, but let's give it to something with stats that aren't quite so godly.
Steel/Ghost but that hasn't been made yet. ( i so want one though, Banette should get it so he becomes a bit more usful)
Edir: Shedninja does too