Looks like there's no specific range or speed restrictions.
According to the
Standard Battle Assumptions, they would start 4km apart. Assuming Gilgamesh can not precisely detect Doflamingo's location, this gives Doflamingo a significant advantage, as he would either initiate with body manipulation with his threads (via the standard direction control method, or Parasito--but the latter is generally only utilized in Bird-Cage, and is more random), and Doflamingo utilizes Kenbunshoku Haki, allowing him to know of the presence of Gilgamesh from very early on. Or he would send his Black Knight, as he generally did in Dressrosa to catch his opponents off guard before attacking himself.
- Side-note: Sha Naqba Imuru confuses me with its functions, if anyone can clarify.
Doflamingo also has the speed advantage, seeing as how he's (way above) nearly double the speed I can see Gilgamesh scaling to.
Gilgamesh may have dura negating attacks, but unless he lands a successful hit that decapitates Doflamingo, it's very unlikely Doflamingo is going down due to the fact he can simply apply his threads to his own body to keep himself alive and repair his organs and tissue over time. Gilgamesh is significantly lower in Durability, so even the Black Knight could possibly kill him if it isn't destroyed first (pretty difficult to do so
considering the BK can fight just fine after having its head ripped off).
Doflamingo has also one-shot several characters scaling over 800MT in durability (Sanji, Smoker, Luffy [twice], and ripping Law's arm off), and considering Gilgamesh's Durability is significantly lower than any of them (basically base-line since I think it comes from a statement of Berserker destroying a mountain).
So basically, here's how it's likely to go down:
Fight starts with both a fair distance away, Doflamingo uses Black Knight (assuming he doesn't use thread manip) and sends it after Gilgamesh. Black Knight is way faster than Gilgamesh and has the potential to take him out on his own, but for the sake of continuing the fight, let's say Gilga destroys it. He thinks he has won, and suddenly Doflamingo hits him from behind with threads or a solid strike and one-shots by either decapitating Gilgamesh, or skewering him completely (scaling <2.5GT to someone with basically 100MT or 385MT durability... yeah that's not even an argument).
It's even worse if Doflamingo chooses to 2v1 with the BK since they're both faster, and Doffy has no qualms of using his own power to take the brunt of the assault, and he'll be analyzing as he fights.
