A common misconception is that you can unlock advanced forms of haki if given enough time, this is false, as Rayleigh mentioned " Haki blooms in life/death situations". So unless you are putting yourself in situations where you'll either progress your haki or die, you are unlikely to awaken advanced forms of haki.
That's why someone like Luffy progresses at an insane rate in learning advanced forms of haki. He is constantly jumping into those life/death situations, e.g.
- He willingly entered a death match against Katakuri to learn Future sight.
- He enthusiastically took part in Queen's games knowing he could die, all in order to learn Ryou.
- He kept on fighting Kaido despite knowing that a very high possibility he would die.
I doubt Doflamingo was out trying to challenge strong foes like Kaido in order to progress his haki, he most likely was training
his devil fruit, which is why he is awakened.