Best order for fate locked stories?

Is there an ideal order you should play fate locked stories in? Or things you should do in the normal game before playing certain fate locked stories? I assume they’re mostly stand alone stories, but FL tends to tease out revelations in a well planned progression and I wouldn’t want to jump too far ahead.

They’re stand alone. Some of them are in short series of three, but they have an overarching theme or commonality. Not an overarching story.

Agreed, about them standing alone.
Many of the Fate-locked stories are about different aspects of Fallen London, and if we include Exceptional Stories then there are certain actions which may be unlocked by decisions in other fate-locked stories. (For example, I believe the Last Dog Society (August 2015) has an option which requires a certain decision made in The Gift.) But it doesn’t hinder progress or deny you any story if you don’t have the appropriate quality, so don’t feel that you’re missing out.

The two I would suggest are the Soul Trade (a.k.a. A Trade in Souls), and The Blemmigan Affair.
Ultimately, though, pick whichever stories are most interesting to you.
edited by Kittenpox on 3/31/2016

Most Fate Locked stories are stand alone, and don’t require each other.

The Fate-Locked part of the Labrynth of Tigers requires something from Flute Street to get the final reward, but both are interesting, so its not that bad.