I think Donquixote Doflamingo's ability isn't a Devil Fruit. I think it revolves around strings which are tied to his fingers and are imbued with Haki. He wraps them around his opponents limbs and controles them and he can pull them so hard that they sever a limb, as seen with Oars Jr. Reasons for this:
-he mostly uses his fingers in a fight;
-his fingers movements are very complex in comparison to other characters and they look 'special';
-he would not be the first anime character to use strings to such extent, as i've seen in other anime series;
-he is never refered to as a Devil Fruit User. The only sure thing that is known about him is that he has the highest bounty among the Shichibukai and is very powerfull, powerfull enough to fight in the great war and end up without even a scar, even dough he fought agains Moria and Crocodile.
-his attacks work against Moria and Jozu but not Crocodile who is a Logia type(logically strings can't affect Logia types). Maybe he didn't use his Haki against Crocodile because he was hopping he would join him eventually.
Thanks for reading this. If you have any comments please write to me. Ja na
edit: given his arrogance (as seen with all Logia types) he could be an unussual logia type, like blackbeard. but i remain with my belief that he's not a devil fruit user.