Do we have anything official on how often we'll be getting them?

Closest I've seen to anything official is that the fiction articles, as recently as the Scorpion fiction, have said:

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Be sure to check the Fantasy Flight Games website every other week for new Legend of the Five Rings fiction!

Assuming that will continue to be the case, and assuming that the "A Most Suitable Teacher" fiction doesn't "count" due to being the fictionalized results of the Kiku Matsuri story decision, I would look for a new fiction to be released sometime next week. Though there could just as easily be a longer gap due to the reduced gap between the Unicorn and Scorpion fictions' releases. If that's the case, then the next fiction would be released the week after next.

So, probably we'll be getting new fiction every other week, resuming in 1-2 weeks.

Plus, I seem to recall them stating that a short fiction would be in each Dynasty Pack, in addition to the above.