Into The Abyss

If you are high level and cannot unlock the portal and cannot find the quest anywhere to start Vashj'r, go to the Hero's Call Board as indicated. If the Vashj'r quest is not one of the three listed, do not despair. Accept one of the other Cata quests, and then the Vashj'r quest should appear on the Call Board screen. If not, keep accepting other zone quests until the Vashj'r quest shows up. Accept it, then off you go!

However, if you have started ANY of the Battle for Lordaeron/BfA starting quests, even the breadcrumb quest in new Dalaran, you will be phased out. I had no uncompleted quests in my log, but I still could not interact with Recruiter Burns to start [Hero's Call: Vashj'r!]. A GM told me that was because I had taken the above breadcrumb so was phased until I completed the whole starting BfA line. I talked to Matthias Shaw on the dock, skipped the Lordaeron cinematic, talked to Anduin in SW throne room, skipped the Jaina cinematic, wound up in Boralus, did the first quest to tag the inn, FP, etc, the was able to go back to Stormwind and do Hero's Call: Vashj'r to open Vashj'r.

I don't think this quest is available.

I tried getting it on an 80 who had not done any of the Vasjir quests, and it was unavailable no matter what combination of pre-quests I had. I even started by abandoning A Personal Summons just in case.

Guide to Vash'jir Kelp'thar Forest Alliance Quests:

Optional Pre-quests:
A Personal Summons and Eye of the Storm
Either Into the Abyss: or Hero's Call: Vashj'ir

Main chain:
Call of Duty
Sea Legs (At any time, kill a Slitherfin eel to start Once More, with Eeling)
Pay it Forward
Rest for the Weary
Buy Us Some Time & Travelling on Our Stomachs
(Be sure to kill a Sabreclaw Skitterer to get Crumpled Treasure Map which starts Kliklak's Craw)
To Arms! and Stormwind Elite Aquatic and Land Forces
On Our Own Terms
All or Nothing
Better Late than Dead
The Abyssal Ride
Good Deed Left Undone (optional)
Gimme Shelter! (also unlocks A Case of Crabs)
Ain't Too Proud to Beg
(which also unlocks A Girl's Best Friend and A Taste for Tail)
This is a convenient time to do The Horde's Hoard, which starts
from Tattered Treasure Map, dropped by Clacksnap Pincer

Next comes Can't Start a Fire Without a Spark

This allows for the optional quest Nerve Tonic, and the optional Bud Chain:

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• Oh, the Insanity
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• Dan, Nunt... Dah, Nunt...
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• Shark Weak,
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• Dun-dun-DUN-dun-DUN-dun
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• A Bone to Pick
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• Decisions, Decisions
• 
  

Around this time, kill Gilblin Collectors and hope
Lady La-La's necklace drops for Lady La-La's Medallion. There are conflicting reports of what quests are needed for the item to drop.
This is also a good time to kill Gilblingle for waterlogged journal which starts Blackfin's Booty.

The main chain continues:
Ophidophobia
A Desparate Plea
Undersea Sanctuary
Spelunking
Debriefing
Wake of Destruction
(also unlocks What? What? In My Gut...? and Decompression)
Come Hell or High Water (While in naga camp, pick up How Disarming)
The Warden's Time is auto-given when Come Hell or High Water auto-completes
Across the great Divide leads to the Shimmering Expanse chain.

Don't forget to group up or come back at 85 for
An Opened Can of Whoop Gnash