I'd first e-mail the author of the other fic to explain the situation and ask their permission for me to post my story. If they nixed the idea, I wouldn't post my piece. If they said they wouldn't mind my posting, I'd then ask them their preference of a posting schedule for my story, and again I would abide by their wishes. If they had no preference, I would wait until a month or two after their story had been completely posted before I began posting mine. I would also explain the complete situation in my FDK thread, and would link to the other author's story. If it seems as though I am treading overly carefully in this hypothetical situation, it is because I'm always petrified of unintentionally plagiarizing or seeming to plagiarize another author's work. (I say "unintentionally" because I would never knowingly plagiarize.)

Joy,
Lynn