I came back in and tested it again. Now there is a down draft again, not as much as when I opened it up initially, but still pushing back the match flame. So I put the hairdryer in the opening for ten seconds and the match flames were going up again, and were still going up a few minutes after that. I suspect that the flow got reversed when an upstairs sliding door was open for awhile.
I'm hope this amount of negative pressure, if a hairdryer can change it, and the flue pipe is still cold, can be overcome by the BK on slow burn.
I would expect any issue to mostly present itself during a cold start. This would be an issue with any stove hooked to that chimney or none at all. Once even slightly warm, you have shown that the flue flows in the right direction. Out of habit, I squirt some torch heat up the flue of both of my stoves before turning the torch onto the kindling to start a fire.