The higher the frequency, the lower the light level before you might see flicker.
LED dimming is PWM ; a square wave.
When you dim an LED, the off time becomes longer and there is a greater likelihood of a frame being captured in an off moment of the LED.
The frequency needs to be at least several times the camera frame rate to ensure no dark frames.
I'm not sure if there is any disadvantage to running very high frequencies.
I would experiment.
An interesting thing to look for/at is a stobing effect to the eye.
Is you run the fixture at a low output and rapidly swing a drumstick in the beam, you will see several images, rather than one blur. Raise the frequency and watch the images get closer together.
Increase the output and watch the images get fatter.
Fun times!
Also, my experience with LEDs have shown that your eyes want a much brighter light than the camera does. The camera CCDs and the fixture LEDs have similar RGB-ness (technical term), so the light capture is more efficient than our eyes with the RGB.
You will probably need to stop down the lens to keep the image from blowing out.