I suspect that your problem has nothing to do with refresh rate - unlike CRTs, TFT LCDs just don't flicker in time with the refresh rate (try setting the refresh to 30Hz - still no flicker on static images).
Rather, the likely cause is some TFT displays' use of Pulse Width Modulation (PWM) to control the brightness (i.e. they dim the backlight by turning it on and off very rapidly, and adjusting the onff ratio). That does cause flicker - especially as you dim the display. "Flicker free" displays use other methods of dimming or use PWM with a very high frequency base - odds are your 120Hz refresh displays, being upmarket, are flicker-free, but PWM and refresh rate are quite separate issues.
I can't find a straight answer on whether the 5k iMac display is technically flicker-free - I haven't noticed any flicker.
Thanks for the information about "PWM". Are there specific types of monitors that don't have this issue?
Also, I'm interested in whether I can drive an external monitor from my 2017 MacBook Pro 15 inch (Radeon Pro 560)? I've stopped by a few Apple stores and nobody seems to be able to give me a straight answer.