Formula for LED refresh rate?
Going back to the old video standards (such as PAL or RS-170), the refresh rate was 25 frames per second or 30 frames per second (depending on where you live). 

The refresh rate was chosen to be as low as possible (to keep the electronics reasonably inexpensive and achievable) but high enough so that the viewer did not suffer distracting (and possibly to some) painful flicker sensations.

These standards were interlaced, so 20msec between one device turning off and the next turning on should work.

In what I currently do, we consider that 5 msec is not resolveable by the human eye. That basis should let you answer your question.

As an example of where we deliberately flicker an LED but it gives an appearance of continuous operation, see this previous question.