Incoming long ass post
Doflamingo is arrogant, but he isn't at the level in which he'd simply let his opponent have the upper-hand. In his fights, he makes sure to avoid taking unnecessary damage whenever he can, and immediately cripples his opponent (against Law, Luffy [pre Gamma-Knife], and Oars Jr). Askin and Doflamingo are both combative experts and geniuses, but Askin is also quite arrogant with his power and his carefree nature has left him open to attacks.
Askin's Regenerationn is at a low level like Doflamingo's. Sure, he can heal from gashes to his body, but attacks that remove his limbs/head, leave a gaping hole in his torso or head, or leave his body in tatters would kill him.
Doflamingo's physical blows and thread attacks can already decapitate (as he removed Law's arm, Oar's leg, and [if not for Luffy] Kyro's head), his Awakened threads can shred and pierce Askin's body completely (poor Colosseum fighters).
Of course, he likely would not use his awakened threads to attack at the start if both are not knowledgeable of eachother, but in the case of knowledge or bloodlust (or both), Doflamingo definitely would try to end the fight quickly.
I could strongly argue that Doflamingo uses Everwhite to give himself the ground advantage, or his Kumonosugaki as an aerial advantage, and once he limits Askin's physical movements, land Parasito and use Goshikito/Athlito/Overhito to decapitate him in one blow.
Doflamingo is a fighter that lets his enemy attack first while he observes before actually throwing his own attacks, or uses tricks to break through their guard (Against Luffy in Round One, Kyros, Sanji, Oars Jr., and Atomos). He never fights head-on unless he is confident that he will prevail.
Unless Askin initiates the fight (Which I doubt since he is even more passive than Doflamingo), Doflamingo will initiate with Parasito or Black Knight and take care.
With no knowledge and this being a standard fight: Could go either way, but Doflamingo may prevail due to his tricks and potential to one-shot.
With knowledge: Doflamingo will instantly turn the entire battlefield into threads, which will force Askin to fight in the air, and Doflamingo can use Sora no Michi to eventually surround Askin, Kumonosugaki to restrict his aerial movements, and Flap/God thread to finish him in one blow.
With Bloodlust: Askin has a chance should Doflamingo briefly drop his guard, but Doflamingo still has pre-cognition and enhanced sight to boost his reaction speed. Doflamingo still has the potential to one-shot here and Askin, not knowing the details of Doffy's power, would likely fall prey to Parasito.
I know that Askin can one-shot Doflamingo with poison, but unless he can find a way to successfully break through Doflamingo's Awakening and pre-cognition, that is unlikely to happen, while Doflamingo can catch Askin with Parasito, Kumonosugaki, or Everwhite before throwing one of his own attacks
And Giftball deluxe will kill Doflamingo even if Askin dies, unless Doflamingo can get out of it with his powers, or Askin doesn't even use it.