Combined with Luffy's CoC, it shook all of Dressrosa and blasted Law away from the area around the source. If Doflamingo applied it to his strikes, it alone would be able to slightly damage Acnologia. Combined with Armament haki (Doflamingo's being fairly proficient) and Doflamingo's kicks (each regular kick capable of dealing casually dealing at least city level DC (http://www.*************/manga/one_piece/v69/c745/7.html the kick cleanly cutting through three palace towers and still spreading outwards) and most likely capable of decapitating Kyros, who is at likely City Level durability.
Without haki, Doflamingo could casually defend and attack Sanji successfully, he was also capable of Defeating Trafalgar Law with Low-Mid difficulty with little to no haki (no haki was shown being used during their first fight) and with mid difficulty during their 2nd fight when both were no longer at 100% of their stamina with minimal use of Armament haki(Law being hurt via lead bullets and injuries and Doflamingo taking a Red Hawk with no protection)
With haki, Doflamingo's attacks were easily capable of breaking base and 2nd gear Luffy's guard and deal significant damage to him if not send him flying several dozen meters (http://www.*************/manga/one_piece/v69/c745/11.html , http://www.*************/manga/one_piece/v69/c760/12.html)
With Armament and CoC haki and attacks infused with strings (while also being injured via Gamma Knife), Doflamingo was able to send a Luffy (who was guarding with haki infused arms) flying for what could have been several hundred meters or even over a kilometer if Trebol had not caught Luffy (http://www.*************/manga/one_piece/v69/c782/12.html)
With Conqueror's haki (Luffy and Doflamingo's kicks being clashed together, so the only force being sent outwards was being their Conqueror's haki), Doflamingo and Luffy both sent Law away from the immediate area of the source by over a dozen meters while also causing the entire palace to be decimated while also shaking all of Dressrosa with its force (http://www.*************/manga/one_piece/v69/c782/5.html , http://www.*************/manga/one_piece/v69/c782/6.html , http://www.*************/manga/one_piece/v69/c782/7.html)
To answer your question, yes, Doflamingo would be able to hurt Acnologia with CoC haki especially if Doflamingo remains mostly unharmed. As Rayleigh stated, CoC's level of power can only be enhanced as the user grows, which means that a fully ready Doflamingo's CoC should be superior to what he used in his fight with Luffy, especially since he was lethargic via Gamma knife and exhausted due to all the damage he accumulated over the course of the Dressrosa arc.
Acnologia is powerful, so CoC's force would only be "felt" by a small degree unless Doflamingo physically struck him with it in conjunction with a kick. It wont be hard for Doflamingo to whittle Acnologia down especially since they are both fairy arrogant and Acnologia's best clocked speed is around Mach 400 while Doflamingos accepted LOW END is Mach 637 and he is probably able to be well over Mach 900 in attack and reaction speed with travelling speed being almost on par (being able to react to Luffy's 2nd Gear 4th strike via applying Haki to the side of his head the attack was coming from: http://www.*************/manga/one_piece/v69/c784/17.html and being easily able to evade Luffy's 3rd Gear 4th strike from a short distance and being able to counter attack: http://www.*************/manga/one_piece/v69/c784/19.html)
Doflamingo should be able to take this especially since Igneel could give Acnologia a very hard fight and Doflamingo has the environmental advantage via Awakening and Bird Cage and that he can fly so long as there are clouds or other objects he can attach his threads to.
Doflamingo is most likely to win this bout