BFG Burning
BFG gets burned basically in two ways (besides team tokens burning); 
1. Auction
BFG used to bid in auction gets burned. This seems to be a low amount, but any burned BFG is good of course ;) 
2. Players losing BFG
Officially they just state that won BFG comes out of team pool and lost BFG gets burned. This doesn't seem to happen on a daily basis though, as this would be unsustainable I would think. 
So, most likely it works just like the cashback mechanism; During a certain time window (month in the case of burning?) the won BFG and lost BFG are sort of pooled, and at the time of burning the net loss tokens will get burned. If there is a net gain, the BFG comes out of the team pool. 

BFG Burn of July
So we just had another (the 20th) nice big burn of 16,822,608 BFG, bringing the total burned tokens to 1,362,830,677. This is almost just as much as there are BFG in circulation right now! 

So please keep gambling those BFG, it will be good for the value of the coin and for all of us :P