All circle AoEs follow the rule that they go off a pulse of the caster. The 3 second timer follows after the *tick* of the users pulse. This is basically how sacred soil works, if you miss the actual pulse tick, you won't get the sacred soil buff until the next tick is supposed to occur post 3 seconds. The pulse in question is determined from when you load into an instance or area.
http://www.reddit.com/r/ffxiv/commen...ming_research/ -> Info here.
So ultimately it, if you were to reapply shadowflare on the tick exactly, the formal SF will tick and then the one that comes to replace it will tick as well in theory.
Sleigh was saying he tried that but it didn't actually do it, while I've seen other people claim that it's true and can be done.
EDIT: I'm starting to think this is under a perfect world scenario instead of reliably happening in game. Editted the OP regardless with a link and a disclaimer for that.
