This appears to give a lot of information on LED latency:
https://electronics.stackexchange.com/questions/86717/what-is-the-latency-of-an-led
Phosphor LEDs, like the white ones in flashlights, are the slowest responding, typically in the hundreds of nanoseconds range. But most LEDs are quite fast.
The components driving the LED often add more latency than the LED itself, with parasitic and junction capacitance, trace inductance, MOSFET switching times, being the biggest factors. LEDs used for high-speed signaling are specially designed to minimize parasitic capacitance, resistance and inductance to improve switching times. LEDs used in flashlights don't need to be super fast to respond, and you wouldn't want them to anyway since it would make the flickering more apparent to sensitive individuals. Even so, they are fast enough to turn completely off and on on each PWM cycle, and it's our "persistence of vision" that makes it look like a steady light to our eyes.
In many designs, such as the commonly used low-side MOSFET switching, turn-off time is slower than turn-on time, so the LED fades out a bit slower at turn-off than it rises at turn-on.