Even with an LCD it is possible to, in a way, burn in the display. In LCD it is called image persistence and while it is usually only a temporary thing caused by a pixel going bright for a VERY long period of time and never changing it can become permanent. Never actually seen it but I know it exists.
Any screen that creates its own light will eventually lose its ability to create light and slowly fade. Now, LED technology has advanced dramatically but still doesn't have an infinite life span. Red typically has an MTBF of 150,000 hours while blue and green are 80,000. To put this into perspective though 80,000 hours is 9 years of steady, full power use. Our displays aren't run at full brightness most of the time(at least mine isn't, I find the factory auto-dim works great for me) and change when we navigate or watch videos.
So yeah, OLED displays will eventually fade and die and will 'burn in' an image if you leave it on the same thing for 4-5 years against a black background at full brightness all the time, but will it happen during the useful life span of the phone or even be possible during normal use? No.