I am having the exact same issue on this end. Before the Big Sur update, I was running a LG 27UL650-W 27" 4K UHD LED Monitor with VESA DisplayHDR 400 monitor with no issues. As a prerequisite: I have 32GB of RAM, and a 8GB AMD Radeon Pro 5500M Graphics Card that was custom-ordered with the machine. Also, it is hooked up to an Anker Docking Station (13-in-1), which outputs the sound to my speakers, which are all at least 6' away from the monitor and the Mac to ensure no interference with the monitor (as I saw on a few online reports that sound interference can cause screen flickering....). There are also 3 hard drives hooked up to the Docking Station, along with the Loupedeck CT, all of which are running with no issues.
Now, I've had this Mac and these systems since September of last year, and I'll admit: I'm using this Mac like I've never used any other Mac I've EVER had, which is at the highest and most intense of all the laptops I have ever owned.... Whenever I'd be using this 2nd monitor with the new Mac, the LG screen would periodically (say, every hour, then every 30 minutes after a period of weeks) go to a black screen for about a second, then function as normal. At first, I wondered why that was the case, and to this day, I still don't know why. I thought that it was doing that so it could be sure to sync properly with the Mac (which is a 16" MacBook Pro 2020 with Touch Bar). I also had scaled the graphics to be slightly smaller on the LG Display so I could see more data on the screen (maybe this is why??? Not sure...). Thirdly, one thing I noticed was whenever the temperature (as the office is upstairs) would get above 80 degrees (as this is a work from home solution, where the entire house is running on one air conditioning unit instead of 2), the fans on the Mac would automatically kick in, and get pretty loud whenever the LG Display was hooked in to the Mac. Once it got to 85 degrees, the Mac would automatically engage in a kernel task to protect itself, despite my turning on fans and even opening up the window before this happened.... However, with the Display NOT being hooked in, the temperature could be over 85 degrees, and the Mac's fans don't even turn on, and the Mac's screen continues to function with no issues, even with it hooked into the Anker Docking Station. I thought it was the LG Display causing the issue, so I hooked that into the iPad Pro via USB-C cables, and the Display has been working fine with the iPad Pro, with no screen flickering whatsoever....
However, after the latest Big Sur update (released a few days ago; not sure if this was the issue either?), whenever I hook the monitor into the computer, I get really bad flickering, or a completely black screen on the Mac, along with a green screen on the LG monitor. I've already reset the PRAM and SMC, and that didn't work. I tried an HDMI to USB-C cable (brand new) in all the ports on the Mac, and that didn't work. I also tried an HDMI to Apple 3-prong adapter/dongle (the one that has the USB-C, USB, and HDMI cable connections on it; brand new also), and connected the adapter/dongle via USB-C into the Mac, and that didn't work. BUT, as an interesting note, Sidecar with the iPad Pro 11" has worked with no issues, where I'm able to use the iPad as a secondary display. This is when I've been using it either directly connected to the Mac via USB-C, or wirelessly.
However, when I did Apple Airplay with the Apple TV, and made the screen (which is a 50" television) as a Secondary Display, the Mac quickly did a hard shut down on its own.... All this time, I also have turned off the Automatic Graphics Switching feature in the Displays area of System Preferences through all these tests, and none of it has produced success. Ultimately, I have a pretty expensive LG Display here that I really, really want to use with my Mac, but can't do so because of this screen flickering, and ultimately blackout issue that keeps occurring. I honestly don't know the solution to this problem, as I have never had this problem with my previous THREE Mac laptops that I have owned. It has only occurred (really badly I might add) after this latest update to Big Sur.
If anyone can give me some pointers or something (anything, please!!!!) regarding the solution to this problem, that would be greatly appreciated, as again, I'd really like to use my LG Display, but can't do so because of this screen flickering (and black/green screen) issues, which makes the Mac either freeze or shut down abruptly. Other than that, interestingly, the Anker Docking Station is working just fine, along with the iPad Pro. This issue ONLY happens when I hook the Mac into the LG Display, or use Apple Airplay with the Apple TV. I will even adjust the screen resolution back to its "native" screen resolution to see if that works (but I'm not sure it will)....
