Weird one - As a boosted horde, how do I get to Kul Tiras? Battle board has nothing, no ports that I know of 
You need to do the quest that has you gather 100 war resources to unlock the quests that gives your the ports on Kul’Tiras.
Haven’t checked but I assume you still get it from Nathanos on the ship.
I think Gazlowe will offer a quest sending you to Kul’tiras-- early travel to kul’tiras as long as you don’t complete the quest. 
If you have an m+ portal that can also be used since they are now acct wide.