It's a minefield. The problem comes where LED brightness is varied using Pulse Width Modulation, resulting in a flicker at the PWM frequency whenever the screen is used at anything other than 100% brightness (the flicker will be most obvious at 50%). Typically that's in the 200-400Hz range, which is far too low, and results in visible artefacts (as well as potentially causing eye-strain, migraine, etc).
OLED displays and most LCDs using an LED light source as the backlight are afflicted. It's entirely possible to drive an LED backlight without flicker (or with flicker in the tens of kilohertz that's actually undetectable by humans, rather than undetectable by some subset of particularly unobservant humans), and some do that. This is starting to become a thing that monitor manufacturers are mentioning in their marketing material, but I don't think that's tricked down to fondleslabs, so there's no way of knowing how flickery a given screen is from the specs - they simply don't mention it[1].
Pragmatically, the only way to find out if a screen is flickering is to test it (remembering not to have it at full brightness!). If your eyes/brain are suitably sensitive, it should be obvious. If they're not, you may be able to perceive shutter artefacts by twanging an elastic band or rapidly waving a finger or pen in the light of the display. Otherwise, you'll need electronics to detect it.
(This all goes for LED lightbulbs too, only they tend to flicker more obnoxiously at double the mains frequency.)
[1] Don't confuse backlight flicker with display refresh frequency.
