This is completed inside the Nighthold instance. Why they don't mark it as a dungeon quest? I have no idea.
Flightmaster Volnath is in
The Nighthold: Nightspire
raid. As of 2.15.17, this wing isn't available in LFR. Took me a while to find this info - hope this helps.
Edit - take the Sanctum of Order portal from Meredil in Suramar, then head right past the summoning stone and go down the stairs. That's where the zone in is and if there's a WQ, it will usually pop on your screen and you can use the green button/LFG tool to search for a group running the normal version. If there's an active WQ like there was this week, it's easy to find a group and he's the first boss in the instance.
I am so over blizzard trying to get everyone into guilds and groups ..... some of us just dont want to and all of these quests and dungeons/raids should be available to all on LFR ffs bliztard!(##RESPBREAK##)8##DELIM##Thulm##DELIM##
It's behind the mobs before you go up the stairs to Tichondrius. Go past the captured Suramar guy and he's in a courtyard down some stairs. Thanks to @TheNealls for the info
This quest cannot be completed in LFR. It must be on Normal or higher.
By far the must frustrating world quest, I did four raids and didn't get the achievement only to learn it's Normal and above.
Is This Quest required to unlock the nightborne?
Legion World Quests Overview
The Nighthold Raid Guides and Rewards