@Whackadoodle:
And in the only circumstance we've seen where he had obvious and immediate reason to fear death (that is, continuing to try to kill Smoker with Kuzan protecting him), he backed down immediately.
The next closest instance - the threat of Kaido coming after him - he went to a lot of effort to fool Law to make him think he'd agreed, and his crew commented on the look on his face when Law pointed out that he should be the one who is afraid (of Kaido).
But no, obviously, Doflamingo is fearless, even in the face of death, which is obviously a CoC thing, even though we've been told repeatedly that's a D. thing.
He didn't back down immediately, Kuzan is strong, no doubt, but first Doflamingo disobeyed and went ahead and attempted to kill smoker when kuzan told him to get off. Doflamingo underestimated the speed of his ice ability, but he backed down when he knew fighting kuzan may actually take a lot of time. That's why he said "I don't have time to fight you." This indicates that if they did clash it may last too long and Doflamingo's plan is ruined by then. He then walks right next to kuzan and past him with a smirk and kuzan has that serious face on. Kuzan then goes and say something about how doflamingo can become the next worse thing since sakazuki took fleet admiral position. we also have to take into account that there are an incredible amount of people going after doflamingo. Caesar about to be taken by big mom's nakamas, kaido possibly going after him, the alliance and revolutionary ruining his plans, admiral fujitora trying to dethrown doflamingo, and the whole island that now has their memory restored. All these things are shifted towards Doflamingo alone. Doflamingo's ambition to take care of these matters is stronger than Luffy's ambition to defeat Doflamingo and liberate the island.