Oh, I'm not really thinking of a character that has astounding good luck or anything. This dude is going to be granting luck (good or bad) to others. And yeah, he'll be using some of his stuff to benefit himself too, but all the other Emissaries seem to do that too. What I'm envisioning is something like this:
Fighting on soil during a rainstorm? He uses his Sponsored Magic to throw down a low-grade entropy curse to apply the maneuver SLIPPERY WHEN WET to the scene, which he can then tag to trip his enemy up. Or if they're fighting close to a cliff? Hope the enemy's ONE LITTLE MISSTEP doesn't send them plummeting to their doom...
Alternately...
You've got his buddy dead to rights and are about to fill him full of lead? Hope he doesn't have a LUCKY BREAK and manage to dodge everything. Or perhaps another buddy had to do a little B&E to get some information on the powerful mystical artifact the group is trying to find before the bad guys, and he just broke the last pick he had in the kit he grabbed and is desperately searching for some way out while the footsteps of the night watchman grow closer. It'd really be LUCKY YOU'VE GOT THAT SPARE in that situation, wouldn't it?
And sure, maybe sometimes it's him that needs that lucky break or that lucky spare. Those can still be double-edged swords. Maybe the enemy goes down in the mud, but spends a fate point to tag the aspect to drag him down too. Maybe the one falling off the cliff grapples my dude and tries to pull him down. Maybe the ally that dodges the bullets ends up captured by the enemy and interrogated into giving away vital info on the good guys. Etc. etc. Plus, there'll be all the compels from the fickle lady to deal with.