I'll start by saying, I have the DJI RC for the Mini 3 Pro and it works well. The DJI RC for the Mavic 3 Pro by comparison, does not.
This controller is slow. Changing Fstop or navigating menus, this thing hangs and I find myself hammering the screen with my finger as it's unable to keep up with basic inputs. I've checked and there is not a firmware update.

The map/compass at the bottom left of the screen: I have no telemetry for this, no aircraft heading or flight route, it's blank.

How do I go about flashing the FW of this controller, as it's definitely not working as it should. I just wonder if anyone else is having the same issue.

You can reinstall the firmware by connecting it to a PC with the DJI Assistant software.    But to rule that out why not pair the Mini3 RC to the Pro and see if you get the same behaviour.  

Hi there. Thanks for reaching out, and we're sorry to read about the issue you're encountering. To refresh the firmware of the DJI RC, please use the DJI Assistant 2 (Consumer Drones Series). If the issue remains, you may also try resetting the RC to its factory settings. Just ensure you back up important files before doing so. Please keep us updated. Thank you.

Yes, the RC reacts very slow when connected to the Mavic 3 zero hence I sold mine and stayed with the RC Pro which works well except for when changing from 1X to 3X and &x, that has a bit of lag

Hi @CloudVisual - I gotta say, I suspect that the RC is just underpowered.  Even when just using with my Mini 3 Pro, i would not call it a quick and responsive powerhouse.  For a few drones I have used the standard RCN1 controller with a dedicated android tablet, and that always seemed to be enough, but even that got bogged down by new versions of Fly, drone deploy, dronelink, etc.  I am waiting on a new tablet with some more CPU power but for now the best I have is the RC Pro controllers.  

I think I’ve been a bit lucky to use the RC Pro, so I should expect the standard RC to not be as good, but the lagging, slow responsiveness of the controller is really not good enough. It works much faster with the Mini 3 Pro, it’s as if the Mavic 3 Pro is too much for it to handle.

Guess I’ve got to upgrade the RC.

CloudVisual Posted at 6-3 11:55
I think I’ve been a bit lucky to use the RC Pro, so I should expect the standard RC to not be as good, but the lagging, slow responsiveness of the controller is really not good enough. It works much faster with the Mini 3 Pro, it’s as if the Mavic 3 Pro is too much for it to handle.

Guess I’ve got to upgrade the RC.

Yep.  I think to get the experience you are used to, and require, that is your only real sustainable option.