If you're going to rivet your armor onto your vest (which I wouldn't recommend) you wouldn't be able to access the back of the chest lights to install the battery. You'd have to cut a window into the vest behind the chest plate.
Don't rivet on the armor, either use heavy duty snaps or velcro OR you can epoxy flat-head screws onto the back of the armor, push them through small holes you cut into the vest and screw on a nut on the inside of the vest.