I think it's very loose if at all, since he doesn't do much of the "bad jokes" the joker did play in TDK, for example the fire truck on fire, turning things upside down generally, I'd have to rewatch it to remember the other "jokes" the Joker did in the film.
When Doffy gets sinister, he simply gets blood thirsty and enjoys seeing people fight each other. He doesn't play any real jokes of his own... Not much of a joker at all if you asked me, the title is a little unfit for Doffy. Unless of course the Japanese word which Oda originally used has potential secondary meanings. If anyone who knows a bit about Japanese language could enlighten me on this that'd be insightful.
It's a common cliche that most villains use in fictional stories. There's always a villain putting people's lives on the line for the purpose of their own benefits. This scenario isn't any different from a hostage situation and we've seen that done to death in movies, television, american comics and manga all together. And of course, we have to find any minor or major thing from any fictional source to compare to "The Dark Knight". I used to like the movie, but now I don't, because people literally worship this film as if it was even "original".
See the first "Batman" by Tim Burton and look at the ideas alone and tell me, Nolan didn't just rehash majority of that movie.
Regarding to Doflamingo and the Bird Cage situation, it's a rehashing of classic, villainy and in this case, Oda found his own way to showcase how vile Doflamingo can be, when he's pushed into a corner.