Ladies and gentlemen... the MUT3K FAQ.

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2.7 Should I ask the author of the original item if I can make a misting of
it?

You ought to. Generally, with items like fanfiction, the author will have
felt that they put a lot of work into their 'masterpiece' only to see it
torn down by hecklers. Of course, some have welcomed the MiSTings with open
arms, and only once has an author been furious about it. This is mostly a
judgment call on your part, but if you feel that the author might see the
final mistied work and might care about it, you should send the author an
email about it, and ask him politely about misting his work. If s/he say no,
take it as a no, and go on looking for another item. But if the reply is
yes, or there is no reply after a sufficient length of time, then go for it!
However, do keep the author's reply around, in case s/he retracts at your
posting at a later point.

Do realize that works of fanfiction are copyrighted (even if not implied in
the work), so asking for permission on these is not just a moral right, it's
also a legal one.

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And a little bit from Tenchi's Vault of Anime MiSTings:

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2.5)Things to do before writing a MSTing

 It is recommended that you contact the original author of the work.
This is merely to avoid any potential hostilities from the author. Politely
ask, briefly explaining what you'll be doing, and if he says no, move on
to another item. If he says yes, or doesn't respond for a while, go right
ahead! It might also be a good idea to keep this reply around if he/she
later decides to flame you for it.

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I trust this should prove useful.

--G. Falconar