What the achievement asks
Finish the questline in which Kalecgos rebuilds the blue dragonflight. Account-wide, and it hands over a Pentagonal Stone Table for your house.
It runs from Keeper of the Ossuary to A Peaceful Farewell, and players who have counted put it at fifty to sixty quests end to end. Nothing in it is hard, but it is not a ten-minute errand either.
Where to pick it up
Kalecgos offers the first quest. He is recorded at the Azure Archives in The Azure Span at 39.4 63, and in Valdrakken at 61.2 36.4, so take whichever is on your way. The story then moves you around on its own and you never have to work out where to go next.
If Kalecgos has nothing for you
Two gates sit in front of this chain, and it is almost always the second one.
The first is level 70. The second is the main Dragonflight campaign, which has to be finished, not merely started. Its final quest is Together We Are Unstoppable, handed in to Alexstrasza in Valdrakken. If that one is not in your completed list, no amount of standing next to Kalecgos will produce a quest.
This chain also arrived partway through the expansion rather than at launch, so a character who levelled to 70 in the first months and then stopped playing has genuinely never been offered it. That is the usual story behind "I finished Dragonflight and it still is not there".
What the run is actually like
Story quests, start to finish. No group is needed, nothing is farmed, nothing is random and no step can be failed or missed. You can put it down and come back a week later without losing anything.
What it costs is time in one direction: fifty-odd quests with a lot of dialogue, travel and cutscenes. Most people spread it over two evenings. If you are working through several Dragonflight questline achievements, this is the longest of them, so start it before the shorter ones rather than after.
The one thing worth doing deliberately is watching the ending. The final quest closes Senegos's story, and skipping the last cutscene is the sort of thing players come back to the comments regretting.
Where it fits
One of six under Dragon Quests, a piece of A World Awoken. The other five are separate chains with their own gates, and none of them shares progress with this one.