Don't get any light with small removable parts that the kid can unscrew and eat. Especially small batteries, which can be fatal if swallowed. Sofirn C01S that someone suggested is nice for an older kid but 3yos still try to eat stuff like that.
I don't know if there is still such a thing as a "shake light" but if you can find one of those that is completely sealed, it might be a good choice. Those lights are powered by a moving magnet and capacitor inside, so it will charge up when you shake the light like a rattle for a few seconds, and run for a minute or so until you shake it some more. There are no removable parts, no batteries to recharge, etc. So I always thought they'd be a good choice when this question came up on other flashlight sites.
Keep the lumen level very low. Even a 1 lumen led can be very bright, maybe unsafely so, if you put it right up to your eye. Maybe defocus the beam by scuffing the led up with sandpaper.
There used to be 5mm leds with swirling colors like distro strobe lights. Something like that could be fun.
Added: what about one of those bigger lights that you power by turning a crank? Again you'd want to exoxy down any part that can come loose.