I'll try to post that later this afternoon, but I believe we're actually close to saying the same thing. When I've used the term "Bible flag," I point out that obviously the soldiers weren't carrying around the large family Bibles that were for home use. If anything, the flags are presented, as you suggest, as a keepsake, talisman, charm, or whatever term one wishes to use.
But perhaps the best way to say it is that while all "Bible flags" are small flags, not all small flags are "Bible flags." In any case, it's given me something to think about, and I really appreciate this discussion.