Here’s what a 7.62x63 (“.30-06”) does to level III armor (think basic rifle protection, the kind that would actually stop the round that hit Kirk). This particular one is a large, very conspicuous plate of steel 8.5 mm thick and weighing 4 kg. You don’t just slot this in under your shirt and look inconspicuous.

And it would have to have been hard armor, i.e. a rigid plate. Soft armor 1) wouldn’t have stopped that round (that’d be more like a step down to level IIIA on the high end) and 2) would’ve embedded the round rather than ricocheting it.