Aeroponics is hydroponics.
Aeroponics generally doesn't have medium, and hydroponics is defined as growing without soil.
I'm not sure it's possible to "flush" in your case.
I don't see why you would need to ever flush anyway...
Flushing is to cleans your soil/medium by passing (RO) water through it. Nothing more. This can be done with or without a plant present, before or after a grow. It's something to deal with salt buildup.
It is not done to improve taste.
Ah, you mean, starving you plant of nutrients.
Annual plants don't need help with this. Gibberellin hormones will make this happen without forcing it.
Withholding nutrients will only slow growth and development.
This "energy" I'm assuming you meant carbohydrates (sugars), but theyre not stored in the leaves. They are stored in whats called "sink cells" located in new growth areas (roots & buds).