I flush in hydro, I don't really bother in soil. Even then, I only flush if the plants are still really really green when the buds have matured fully and ripened.
It's not salts and fertilizer in your plants. Your plants don't take up "fertilizer" although they can take up some salts, it's not the salts that are causing the smoking experience that you are referring to. It's Chlorophyl, plain and simple.
In my experience if the plants are yellow and purple and dead when they are harvested, the smoke will be smooth and tasty, if they are really really green and healthy, you will get a lot of harshness from Chlorophyl and a good cure is the only solution.
When the plants begin their natural senesence, triggerered by the change in lights schedules it signals to the plant that reproduction needs to be the #1 priority. If your plants are focusing on building buds and don't have the nutrients available to continue the process in the rootzone they will get it from their own leaves. Drawing down these nutrients from the leaves slows photosynthesis and the production of chlorophyl. The main reason that people feel that flushing provides a better smoke is that it actually forces the plant into this position and being deprived of nutrients it will draw from within and will slow the production of chlorophyl.
The problem is that this is a trade off. Slowing photosynthesis also means slowing bud production as well in the final week(s). The plant is producing less and less energy from the lights and your ultimate yield will be less than if you didn't flush. Some people have a goal of harvesting green plants, and the reason is that the plants had EVERYTHING available to them for the entire grow and grew to their max potential, but often the smoke can a be a little harsh. I have found personally that I like to keep them green as long as possible and feed them less and less as flowering finishes up, but I don't do a full on "flush". It's kind of a balance thing for me. Too green (like the ones in my avatar....but look how BIG!) and they can be a little harsh, but rightly potent, and if they get too jacked up too early obviously yield is dimished greatly.
In conclusion, I understand the process, I see why people do it. It will cause your buds to be a little smoother smoke, but it's not to remove chemicals and/or salts from the plants themselves. It's really to slow the production of Chlorophyl, the enemy of smooth smoke.
This has been my experience and is based on what I've read of plant biology, other annuals and fruits, and from the smoke that has resulted from my years of growing. I am not a biologist and I don't proclaim that this information is 100% accurate. Take it for what you want, but this has been my experience and is where I currently sit after many hours of research on this subject. There's a lot of information and misinformation, but I have looked at tobacco plants, how they are grown and whether they flush, as well as any other fruits/vegetables (although not smoked so I specifically researched tobacco) and I this was the conclusion I've come to.