Here are my takes on organic and chemical fertilizers.
When we used the chemical, powder fertilizer flushes were nice. If for nothing else than to rinse out some of the chemical salt residues on the inside of the pots from the fertilizer. I'm pretty sure that back then, we did a plain water flush for the last watering and then let the plants go without anything for ~2 weeks, then harvested. I don't remember having nasty tasting stuff.
I don't really flush with organics because there isn't any salt residue in the pots, and I don't feed every week. Heck, I don't water every week either. Generally, the last feeding will happen 4 weeks before the plants are cut. 2 weeks before the cut, I'll give a water-only-watering because I dislike to overfeed.
Honestly, other than physically rinsing out residue in the growing medium/pots, I haven't heard a good reason to flush. I don't think plants store excess nutrients in the flowers. Even if we assume a flush does use up extra nutes in the buds then it still doesn't make sense because other parts of the plant will be preferentially eaten up. Evolutionarily speaking, a plant would try to keep the flowering intact as long as possible, those are the parts responsible survival.