I've had great RNG, and sucky RNG.
I got the Onyxian and Azure Drake on the same day using two different alts. (One won one, one won the other.) Maybe ~25-50 kills total on both.
I got the Blue Drake TWICE in three weeks, the second time while going for the Azure.
I got the Attumen's during the 6.0 pre-patch event. Maybe ~100 kills or so on it, but I was farming other things at the time in there for xmog, plus the first boss takes longer to get to Kara than to kill, so not a big deal.
Two weeks ago, I got the Flametalon from Alysrazor, last week, I got the Pure-Blooded Firehawk. I haven't run FL's much, doing it with my wife so she can make Dragonwrath, and she is on the first stage of it, so all told? 4 or 5 full clears.
So, those are good RNG stories.
But Anzu? I have over 200 kills across 12 90's, and still no stupid bird.