The actual contents of the display are stable. It’s the OLED pixels themselves that are flickering on and off. This tells me that the signals and control of the display, and the RAM and control logic of the display’s on-board SSD1306 chip are working properly.
The problem is likely with the high voltage power supply for the OLEDs, which is generated by charge pump circuitry in the SSD1306. It could be connections or circuitry internal to the display itself or the required external capacitors on the module or their wiring. If you have a oscilloscope available you could probe the Vcc pin (28) on the display’s flex cable, to see if it’s the proper voltage and stable.
Anyway, I suspect it’s the display itself that’s bad and not anything to do with the wiring, Pro Micro, or software. Replacing the display module with an identical one would be the easiest (but expensive) next diagnostic step.