The problem isn't the flicker directly (240Hz is above the flicker fusion threshold), it's the phantom array effect when you move your eyes. Static images transform into a series of overlapping images, and this can be annoying and distracting. It's visible well into the kilohertz depending on how strong your saccadic masking is. I can personally see PWM up to about 10kHz (tested using a strobing LED).

AFAIK, all OLED displays have PWM flicker, and for this reason I stick with LCD, where flicker-free displays are available (although PWM flicker is present in some LCD displays too).