No matter how you look at it, all the fact information tells you that, Fujitora is after, Law and Luffy as well as the pirates in the colosseum. There's a small chance that he's checking up on, Doflamingo as well. I doubt he asked for their help. Seems like the issue about SH & HP alliance is their reason. Fujitora, must be heading for green bit because, Smoker told them about it which obviously means they're after, Law & Luffy.
Zoro, might clash with, Fujitora for a bit and we'll see his new strength. Luffy, is distracted, as, Doflamingo planned (I suspect). He's most likely going to show up at the last minute and save everyone's ass by kicking, Doflamingo's ass. Franky, is headed to some "Flower Garden". Seems like the factory is located there. The only place that seems like a flower Garden is green bit. Seems like the best place to hide it since no one can get there except for super strong people and Gnomes. It's perfectly guarded by those crazy fish.