I'm guessing you're talking about a subwoofer, in which case, there wouldn't be any advantage other than a cosmetic one.
Flush mounting only helps higher frequency drivers avoid edge diffraction off of the driver's flange. Since sub wavelengths are so long, the flange is "invisible" to the soundwaves.
Only advantage I see to flush mounting the driver is if you are doubling the thickness of the baffle. The extra rigidity of the baffle board will be a good thing, but you can double the baffle without flush mounting too.