What do you mean "flicker". Are you trying to take a video? Or is it just coming out underexposed like in the first photo?
Is the light fluorescent?
Either way, I don't think the camera has a special setting exactly. You probably know this, but AC lights like incandescents and especially fluorescents pulse at the same frequency as the power in your house (60Hz in the USA and Canada, 50Hz most other places, i.e. 60 or 50 cycles per second). When you get an underexposed shot like that, you're catching the scene in between pulses. You have to be shooting with an shutter speed fast enough to open after one pulse and close before another pulse, faster than. If you set you shutter to 1/60, you 'll get a full cycle. If you're shutter speed is set to 1/125, you should get almost half a full cycle with should have at least one pulse. Try playing with your shutter speed and see if that helps.
Here's a good article for reference:
https://photographylife.com/light-frequency-issue
BTW, the a7iii is a fantastic camera. I have one too. What lenses did you get?