Looks like Ocotillo got most of it right.
1. Yes, a plant can be stressed by the flush, and they often get a little droopy. I use Fox Farms trio of nutes which is notorious for salt build-up, and I flush them all on the first of every month in both growth and flower stages. They get over it.
2. Never compact your soil on purpose. Time and watering will do that for you, but don't rush the process.
3. Depending on size, I "flush" with about 1.5 to 2 times the volume. The larger the pot, the larger quantity I use for flushing. (always use properly ph'd water)
4. If a plant needs a flush, she needs a flush. ...ya do what you gotta do. I will usually transplant about 2-3 weeks into flowering to get in her into her final pot, and will do a final flush just prior to that transplant. (letting the soil dry before the transplant so the rootball stays intact) If problems of salting or nutrient build-up are causing problems...a flush is better than additional stress and damage caused by the issues.
With flushing in flower (during the winter) you can time the flush to occur on a normal watering day, but be aware that flushing will keep the soil hydrated, for a longer period of time. (skip a watering or two till soil is back to 'normal') Watch humidity levels and stress while in flower.

If soil is taking forever to dry-out...more fans on higher settings, and more ventilation if possible.
Don't go 'flush-happy' and overdo it. Constantly wet soil will cause root rot and higher humidity can cause mold...so use common sense.

Also...stinky is a girl.