This is a reasonable concern. Here is what's known:

Camera flash: A kids camera LED flash is nowhere near as bright as a professional camera flash. The LED outputs a few lumens for a fraction of a second — comparable to looking at a smartphone flashlight briefly. It is not considered harmful to a child's eyes under normal use (taking the occasional photo in dim light). Like anything bright, it is momentarily uncomfortable to look directly into from inches away, but it does not cause retinal damage at these power levels.

Screen: The 2.0–2.8-inch IPS LCD screen emits standard screen light. Like any screen, prolonged staring at close range can cause eye strain. The practical limitation is that children rarely stare at a camera screen for more than a few seconds at a time — the camera is meant for taking photos, not watching content — so eye strain is less of a concern than with a tablet or phone.

Best practice: Teach the child not to point the camera directly at someone's face from very close range when using the flash, which is the same etiquette as any camera. Beyond that, the eye safety concern on kids cameras is minimal.