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)....

UPDATE: I also changed the screen resolution back to "native to display" on the 2nd monitor, and at first, everything was working, but then, after 2-3 minutes, the black/green screen + flickering kept intermittently showing up on screen and got worse. But then, once I unhooked the monitor, the Mac continued to function normally (which is how I'm using it now). The screen isn't flickering at all since then.... Sidecar, which I'm using with an 11" iPad Pro, where the display is set to "Use as Secondary Display" is functioning normally.... So, obviously there must be a problem within Big Sur that is causing this to happen. Sidecar on the iPad Pro is working just fine, so that isn't the issue. The problem lies with the "Secondary Display" dynamics on the Mac toward larger screens.... Airplay on the Mac towards an Apple TV (which is connected to a 50" screen) is basically unusable right now, forcing the Mac to shut down almost immediately (after about a minute or so), and without warning. And yep, it's true: Before Big Sur, I didn't have ANY problems running a 2nd monitor on the Mac, nor any Airplay issues. On the iPad, connecting to Airplay via the Apple TV has been functioning with no issues.... Secondly, and this might be something to note: In the past, whenever I was running a second monitor (and this was AFTER Big Sur was installed back in November), if the temperature in the office (which is upstairs) got to about 80 degrees, the fans in the MacBook Pro would automatically turn on. By the time it got to 85 degrees, the Mac would begin performing a "kernel" task, hence slowing down the computer. However, both the Mac and the 2nd monitor would continue to display graphics with no issues.... BUT: Since I have NOT had a monitor hooked directly to the Mac, but yet (still) have the Anker 13-in-1 Docking Station + the iPad Pro running Sidecar, connected directly to the Mac, the temperature in the office has gotten up to as high as 90 degrees (a moment ago), and the Mac is running just fine, with NO fans running on it at all.... This must mean that something either in the graphics processor has not been updated with the latest update to Big Sur, or there must be a bug of some sort that is causing the graphics processors to "glitch" (if that's the word), to cause the 2nd monitor and the Mac to BOTH flicker and display black/green screens.... Windows 10 forums keep saying that the cause of screen flickering has been because of drivers not updating, so the "root" of all this might be a driver update (from another update to Big Sur???) to the graphics cards.... Hopefully Apple will fix this problem. Until then, I can't hook any external monitors to this Mac, as that would render the computer itself almost useless....

UPDATE: It's still persisting. Is Apple aware of this???? Is anybody out here experiencing this too (if not in the same way, a similar way)? And, is there a fix coming for this??

Here is a potential workaround solution for now (as this came from a user in Piunkaweb.com), as I have noticed in the past nearly hour (as of this writing) of usage that there has not been any screen flickering from my Mac or from the 2nd monitor. It is as follows: A) While the Mac is up and running, connect the monitor to the Mac. B) Then, disconnect the monitor's power source from the power outlet ONLY. I waited about 10 seconds or so. C) Then, connect the monitor's power source plug back into the power outlet. Important Note: DO NOT disconnect the USB-C cable (or dongle) from your Mac at all. Leave this in place.... D) Then, I went into the Displays area of System Preferences, and set the screen resolution of the display to "Default for Display." In the Displays dialog box, it should show "Looks like 1920 x 1080". All in all, it seems that this latest update in Big Sur (11.1) has broken support for all 4K monitors, perhaps making this one of the worst bugs in macOS that I've probably ever encountered to date. According to other users, any resolutions that are displayed above 1080p resolution is bringing forth a problem in screen flickering. Thus far, I haven't seen any flickering issues with the Mac or the 2nd monitor since doing this. I am currently "cautiously optimistic" that this is a workaround solution to this problem, as I never had any problems with screen flickering in all the years that I have owned a Mac (going on 16 years now!!!), that is, until the 11.1 update to Big Sur. I must say: This is an absolutely unacceptable situation, given the fact that many of us have spent thousands of dollars on our machines, only to have a problem like this occurring. This affects people very adversely in that making professional presentations can be a problem with our own Macs, along with doing professional work on these machines.... So, in the meantime, I don't plan on updating Big Sur until a) I see that Apple has solved this problem, and b) that other users in the Apple community are seeing that the latest updates do not cause this problem any longer....