So this guy is Law's idol...?
Luffy, with his hands still tied behind his back, is attacked by Bellamy and Doflamingo's string puppet and gets stomped into the palace. Law battles Doflamingo one on one and Doflamingo explains that the World Government cooperates with him because he knows their big secret. Doflamingo also wanted the power of Law's Ope Ope No Mi as the fruit's ultimate technique is to grant immortality at the cost of the user's life. Doflamingo reflects that he gave Law the fruit and his crew taught Law everything he knew about fighting, and Law agrees and declares that he will use what he learned to eliminate Doflamingo's crew.
16 years ago, a young Law, who supposedly will die within 3 years due to some disease, is allowed to join Doflamingo's crew but Diamante and Trebol don't think he'll last long. After seeing the young Buffalo and Baby 5, Law meets Doflamingo's brother Corazon for the first time. Corazon is a strange and clumsy guy who doesn't speak due to some past trauma and hates kids. During the course of Corazon stumbling into the building, he hits Buffalo and Baby 5 and then throws Law out of the building. The young Law vows at that point to kill Corazon.
It's time for Law's flashback, but before that we learned that Doflamingo can still call on the World Government for help because he knows their big secret. That's a secret that'll have to come out eventually, whether through Doflamingo's mouth or some other way. I wonder if the World Government will take the opportunity to eliminate Doflamingo if he's weakened enough. Doflamingo is also after the immortality that one can gain from Ope Ope No Mi, and again that's a plan we'll sure to find out somewhere down the line. Moving on to Law's flashback, so Corazon was the Hearts executive in the Donquixote family. He's a strange guy who tosses Law out a building the first time they met, but Law would eventually look up to Corazon. This flashback will probably take a couple of chapters given its importance in the current story arc.