Elimination of bromide and acetate under reducing conditions
What reaction can lead to this elimination when it seems that no
  proton is leaving the molecule (instead of bromide) and acetate is
  leaving?


This is a reductive elimination reaction.  The classic textbook example is the reductive elimination of trans-1,2-dibromocyclohexane to cyclohexene in the presence of zinc dust and acetic acid.



It is basically a redox reaction where the zinc metal is oxidized and the dibromocyclohexane is reduced.  As with many reactions involving electron transfer from metal surfaces, the mechanism of this reaction is not fully understood.  Perhaps the zinc inserts itself into the carbon-bromine bond as a first step, but in any case, electron flow proceeds in the direction shown above.

The reaction has found many uses and has been widely modified to include cases such as yours where a bromine and another group are eliminated to form a double bond.  Here is a link to a paper where one of the bromines is replaced by an alkoxy group and the same zinc-mediated reductive elimination occurs.  Here is a link to another paper where zinc is used to perform a reductive elimination in a series of compounds where both bromines have been replaced, one by acetate and the other by hydroxyl.