My understanding looking at this Wikipedia page is the B47 didn't show up in the BMW 320d until 2015. It is true the N47 (the B47 predecessor) had timing chain issues, but the was fixed/mitigated early on (it also depends on who you listen to or what you read on the internet). After the mitigation, there were far fewer engine failures due to it, but the N47 continued to experience timing chain stretch which allowed for a noisy engine.
The user CalamariFritti on Boards.ie (who seems to be knowledgeable - Post #12), had this to say:
Chain and tensioner had a problem leading to the chain getting a tiny bit longer over time. In early N47s this could lead in extreme cases to engine failure but most of the time just a noisy chain. When I say early we're talking pre 2010 or earlier even. E90s. Several upgrades to the N47 were made and generally speaking since about 2011 at worst it gets a little noisy now but no catastrophic failures. A little noisy is not much of an issue IMO sitting behind a 2 litre turbo diesel that isn't going to be very quiet in the first place. Since the arrival of the F30 3 series (2012 IIRC with the arrival of the N47T (or was it U or N?)) all should be good. Newer 3 and 5 series don't even have that engine. I think from 2014 or so they sport the B47 (I believe its called).
It appears from what I'm reading, the B47 suffered no issues with the timing chain and the issue in the newer Bimmers is all but forgotten.