Flameout hops go in when you turn off the burner (obviously), but you might think about already having your IC in their for the last 10 minutes or so to sterilize it. You can wait a few minutes to actually start chilling if you want, to let the hops soak longer, but I haven't and it's worked for me flavor-wise.
Leave a spoon in the wort while it's chilling, and cover with a lid if you can. When it's chilled, pull out the IC, put the kettle where you want it for racking to your primary, THEN stir up your whirlpool and let it go for 15 minutes (or longer, I can't remember how long is recommended). The idea is that the whirlpool is the last thing you do, so you don't stir up the trub cone after it's set up.
That said, my last (first) attempt at whirlpooling really didn't pan out. It helped a little, but I probably didn't let it swirl long enough. Just because it looks still doesn't mean there's not still movement beneath the surface.