I would wait for an app team member to respond definitively but in my opinion I don't think it will work. The flak vest will need to be relatively form fitting but the gathered elastic at the back of the jacket won't let your armor lay flatly. If you remove the elastic, there will be excess material and you will need to sew in darts which seems more effort than what it's worth if you're looking for a no-sew flak vest option.
I've definitely seen people do something similar with other jackets but I don't know if you should try it out with this one in particular.
