This has been possible in RetroArch for a very long time, but it requires twiddling a few esoteric options that may not be familiar to a majority of users, so I figured I'd run through the process briefly.
Step 1: Flip the screenAs with most of the fun video tweaks in RetroArch, we accomplish this through a shader. So, with some content loaded, bring up the 'quick menu' and scroll down to 'shader settings'. On that screen, increment the number of shader passes from 0 to 1 and where it says 'shader #0 N/A,' navigate to the image-adjustment shader located in the 'misc' subdirectory of your shader flavor of choice. I'm using slang shaders here, which are compatible with the Vulkan and D3D11/12 video backends. You can add additional shader passes after the image-adjustment shader, if you like.
Step 2: Flip the controlsFrom the shader menu, hit backspace or 'cancel' to return to the 'quick menu' and look for the 'controls' submenu. Here, you can change which of your physical or retropad buttons trigger which core functions. So, scroll down until you see entries for the D-pad. In my case, we have 'Left D-pad (key: left)', to which is assigned D-pad Left, and 'Right D-pad (key: right)', to which is assigned D-pad Right. Simply swap those (as pictured) and you're all set.
Bonus Step 3: Flip the audio channelsThis is not vital, but if you want to get the full mirror effect, we'll need to swap the audio channels so that the sound effects follow our mirrored video and controls. This is achieved using RetroArch's fun, powerful and oft-overlooked audio DSP system. The pre-installed 'panning' DSP has the ability to swap the channels, we just need to create a preset file that tells it how to do it. So, open up a text editor and paste in these contents:
filters = 1Save this file as something descriptive and change the file extension to 'dsp' (mine is named Mirror.dsp) and then move it into your RetroArch installation directory, under [RA dir]/filters/audio. Then, back out of the 'quick menu' and go to 'settings' -> 'audio' and scroll down to the 'Audio DSP Plugin' option, where you can select your newly made DSP preset:
filter0 = panning
# Swap left and right channels:
panning_left_mix = "0.0 1.0"
panning_right_mix = "1.0 0.0"