As there is currently no way to tell the correct order of the quests i decided to create a little csv-file containing some additional infos.
You can download it from here: http://filedump.gw2info.net/quests_order.csv
It's just a very simple CSV with the following columns:
Let me quickly explain the "order"-field. Its just that: a field by which you can order the stories and get the correct order. Quests from different storylines that are at the same "logical position" inside the whole storyline have the same order: for example "Hunters and Prey" (Order of Whispers), "Stealing Light" (Durmond Priory) and "Marching Orders" (Vigil) all follow after "Further into Orr". FiO has the an order -value of 42, therefore all those quests have an order-value of 43.
While you can easily order the quests of a player using this field you can't use it to display/reconstruct the whole branching parts of the story (that's what "Followed By" enables you to do).
Let's hope that something like this gets added to the /v2/quests endpoint
Disclaimer: While I did a lot of checks to ensure that everything is correct, its a LOT of stuff with a LOT of branches. So there might be mistakes - if you find one, please report it here and i'll update the file.