No, you don't have to flush. But as the alternative, just water with plain water for the last 1.5 to 2 weeks before harvest if you're worried about any taste from some of the wacky high residue ferts available.

Molasses, no, why bother. Add molasses to the soil early on, to promote soil flora and fauna that will be beneficial to the plant. Carbohydrates do not get absorbed by the roots of plants.

Try this test: flush one pot, leave the next. Harvest, dry, smoke. save the completely burned ash, and you see if you can taste the difference.
I didn't think so.

Now go and check the heat of vaporization for different inorganic and organic salts.

Why does organic outdoors soil taste good? You certainly can't flush the earth.