City of Data has numbers on the combo effects, although the language used is a bit cryptic. Still, I think this page answers your question as far as the effects of sweep: http://tomax.cohtitan.com/data/power...des.AoE_Bridge
It looks like Typhoon's Edge basically does 50% more damage when closing sweep than when used on it's own.
I would guess it's similar to the ST one in a sense, that it's BF>Sweep instead of BF>AV. With burn I would tack it on at the end and just be glad that it lowers the needed recharge to run that. Of course, I haven't checked, so it may not even need much recharge to run.
For single target, I know BF > AV combo is the sweet spot for Dual Blades, but what about AoE? I can't seem to find the numbers/stats for the Sweep combo effect, so it's hard to crunch out the best chain. Has anyone done this with Burn in the combo?