There is definitely a significant amount of "cross pollination" that has happened over the years, but I don't recall seeing any Fluke-branded handheld or clamp meters that looked like anything Brymen has ever made.
Wavetek-Meterman-Amprobe rebranded some Brymen meters for sure, however (I have a few), and of course Fortive owns both Fluke and Amprobe currently. Some of Amprobe's current models are Chinese imports.
There is a good chance that parent company Fortive makes various deals with other manufacturers including Brymen, and obviously Brymen does the same, because Brymen doesn't make Alkaline batteries or cardboard boxes, for example!
So it's possible that when Fluke wants to build something they may consider obtaining some parts from Brymen. I doubt it's the main PCB assembly, as that might help Brymen discover something Fluke doesn't want them to, who knows. Some of the Fluke probes are made by Chinese manufacturers. So Brymen might make something for Fluke somewhere in between those two extremes.
I purchased a Greenlee DM-210 (a rebranded Brymen BM202) over 20 years ago from a local electrical supply place. I remember wanting it because it had a computer interface, which I used with my laptop and it was quite a bit cheaper than Fluke. I think the only other DMM I had at the time was a Micronta 22-167 (all the others were analog).
While Greenlee pricing is slightly higher than direct from Brymen, it's not outrageous especially when you consider many Greenlee prices you see online are retail prices (and you do get the lifetime warranty). If I go into my local store and ask for contractor pricing, it can be 10% or even 25% below retail in many cases.
So Brymen (via Greenlee) in the US has enjoyed quite a bit of exposure over the decades, but they really were never that popular IMHO. I don't think Brymen (Greenlee) ever really was a direct competitor to Fluke, more like a budget brand back in the day. But these days, "budget" typically means a low-cost Chinese DMM, which Greenlee does sell as well. So this means even less of a chance for Brymen probably.