its actually better to flush with a low ppm nute solution or one of the way overpriced flushing products on the market.
Two reasons:
1. ion displacement. Salts are held by the soil media because of ion attractions, its easier to displace ions if you have some other ions to knock them loose.
Similar to the reason salt is used to flush ion exchange water purification systems. but don't use salt
2. You don't want the roots in a complete ionic void like distilled water. Negative osmotic pressures are not good for living cells.
Its kind of like the reason for using saline as an intravenous fluid, or a sports drink instead of plain water.
Assuming you have decent tap water , i would use tap water instead of distilled water.