What are the specific number of passengers and conditions required to select HI, NORM, or LOW on the pack flow knob?
From the A320 flight crew operating manual (FCOM):

  

The selector is kept to NORM in most conditions.

It can be turned to LO:


When the number of passengers is low. 115 passengers is indicative and there are local regulations about the quantity of air which must be delivered per passenger. Operators may have different instructions in their SOP.
When fuel is low for some reason. Using more bleed air increases fuel consumption.
It is also tempting for an operator to reduce fuel and maintenance costs by also reducing air flow. See this thread on PPRuNE.


Air flow can be increased to HI:

Automatically:


When the other pack is turned off.
When APU provides bleed air.


Manually:


When air is too wet due to perspiration and breathing. Dampness increases with the number of passengers.
Air in the aircraft contains smoke.
To intentionally increase tapping of bleed air from the engines, which increases compressor stall margin. This would be desirable while flying in a volcanic ash cloud.


Packs also provide air for pressurization purpose (PACK stands for pressurization and air-conditioning kit). In case of leakage, air flow can be increased. In emergency situations, bleed air can be replaced by ram air (ram air is normally only used for cooling bleed air, but doesn't enter into the pressurized sections of the aircraft).