How fast should I feed 74HC164 for driving LEDs?
The loading on Q7 output of each shift register (except the last) will affect the propagation delay of this signal into the A and B inputs of the next shift register. You need to make sure that the clock period is longer than the sum of


the maximum propagation delay of the Q7 output, plus
the minimim input setup time of the A, B inputs.


The propagation delay of the Q7 output will depend on the supply voltage and operating temperature range, which you have not specified. This delay will also depend on the loading of the resistor and LED connected to Q7. I checked one manufacturer's data sheet and found that the Q7 propagation delay was specified with a capacitive load of 50 pF but there was no information about how the delay varied as a function of the capacitance, and the data sheet assumed that the load was purely capacitive (no d.c. current). Therefore, the data sheet did not provide enough information to answer your question. My guess is that you are just going to need to build the circuit and measure the Q7 delay under the specific conditions you intend to use.