ive never tried it but the last statement in your post is just hilarious
By the time you'll be done activating Burn, most of them will be back on their feet and some will run out of the patch before you finish Sweep to KD them again.
They will run in and out though, just don't expect to keep all of them in all the time.
Thanks for the replies.
Nihilii: That's about what I had expected. The activation times on Burn and the rest of the Sweep combo will allow some enemies to escape. I was looking through the rose-colored glasses of my DB/Nin stalker who could Sweep/Caltrops/1K Cuts for sadistic glee. It wouldn't be an every-fight strategy, but if a teammate impeded the enemies' movement somehow, bad guy stir-fry might still be fun.
Swift Frost: Glad I gave you a chuckle 
Hello all,
I'm thinking about rolling up a DB/FA scrapper because the idea of keeping Blazing Aura buffed with Blinding Feint looks intriguing. However, I'd like to hear back from anyone who's tried leveraging Burn with the Sweep combo. Here are my thoughts: launch 1K cuts to knock down targets, activate Burn (won't break combo because it's not another DB power), enemies are on fire while on the ground, finish Sweep combo to knock them down again for more toasting.
Thanks!
Actually, maybe I just want to try that combination and yell, "They're done on this side - flip 'em over!"