Well in my experience if Kingdra is special then Empoleon does a great job of walling it (it's usually 252/252+ SpD after all). Empoleon can't do much back, but I'd still go for the burn and wear Kingdra down. It's not like Kingdra will deal much damage to Empoleon anyway; it needs something like rain Specs Hydro Pump to deal serious damage (and it's not even that serious). If Kingdra is physical then Empoleon takes more damage, but Kingdra needs to boost to deal that damage and it cannot do that safely since Empoleon will always be threatening a burn. Finally if Kingdra is one of those RestTalk or ChestoRest variants, Empoleon can phaze, which with 5th gen sleep mechanics means it'll have some difficulty waking up and / or make Kingdra waste its Chesto Berry.
I can't see Empoleon losing to Kingdra unless Kingdra is the last Pokemon, when Empoleon would at least be able to get some damage in (unless Kingdra has Rest) and possibly burn. I suppose if Empoleon gets worn down over the match, it is vulnerable, but then that means Lugia can't wall Caterpie because it can get taken down to 1% health and die on the switch-in to Tackle ...
I can't see Empoleon losing to Kingdra unless Kingdra is the last Pokemon, when Empoleon would at least be able to get some damage in (unless Kingdra has Rest) and possibly burn. I suppose if Empoleon gets worn down over the match, it is vulnerable, but then that means Lugia can't wall Caterpie because it can get taken down to 1% health and die on the switch-in to Tackle ...