From what I gather of those straps, they're primarily meant to be worn so camera hangs on the right. The default for actual messenger bags is to be worn on that side as well (Ironically-enough, when I rode courier, I rode with my bag worn goofy cause of years of wearing a camera bag on my left,
) but you can do either.
I'd guess you'd want to wear the strap under everything, any jacket included, and then wear a bag on top of everything. I have always slung out-of-bag cameras on the same side as the bag, if they weren't in my other hand: only way to thread through crowds and obstacles without clashing into things. It's how I'd do it.
That way the left hand (behind me) can guide and retain anything slung on that shoulder, bag and-or-slung camera) while the right, usually held higher, is usually up around my shoulder and leading the way with either the camera or my elbow. I think you could arrange one of those R-straps so that you could do this. (Cause I've thought about it.
If that makes any sense.