Law made Doflamingo choose between angering Kaido or giving up everything he built in the past 10 years being hunted by admiral
s (Plural):
When Doflamingo decided to give up everything and being hunted by admiral
s, Law, who didn't know of Doflamingo's heritage, said, that Doflamingo had no other choice, it was the only option:
Giving up everything he built and being targeted by multiple admirals is, according to Law, a better outcome as compared to having a kingdom, a lot of wealth and immunity from the Marines while potentially angering Kaido by being unable to deliver a product.
That aligns with the fact that Aokiji encouraged Smoker to have Akainu dispatch the admirals (again, Plural) and Aokiji not being bothered to attack Smoker in Aokiji's presence and straight out attack Fujitora, being confident that he would be able to get rid of him, while being terrified to the core just hearing Kaido's name.
Doflamingo seemingly has no problem facing admirals and being "hunted" by them, as he has no problem blackmailing the leading figures of the WG, namely Imu and the Gorosei, saying they tried hard to kill him but couldn't.
How can Kaido as a single man cast so much fear and terror into a man that isn't afraid of blackmailing the entire World Government and being chased by their "strongest military force"? How strong is Kaido? Is this the reason Orochi was so confident in front of Cipher Pol Aigis Zero, saying there is no reason to be afraid of the WG as long as he is backed up by Kaido, shooting them into their mask and demanding, with the CP0 getting visibly nervous?