Salt water flushes, drinking large amounts essentially as a purgative has no health benefits. We do similar things to prepare patients for diagnostic tests or surgery, but not because we are "flushing out toxins"...just cleaning out the poop for a colonoscopy, for example. There is a slight risk of sodium overload.
You're "sick". That could cover a lot of things, but I assume you mean you just have a cold or the flu. These are both viral infections and flushing out your GI tract will not make any difference at all, you might actually feel worse. What is it you think is there that needs flushing out anyway? There are no "toxins", no parasites, no poisons, and your body has evolved vary efficient ways of disposing of the normal waste products of metabolism. It is even pretty good at dealing with small doses of real toxins (not the mythical ones Alties vaguely refer to)
In short...you would be wasting your time and might make yourself feel worse. A salt water purge has no health benefits of any sort at all. If you have a cold or the flu, it will get better in its own time.
Amber123 has no clue what she is talking about with regard to detoxes and flushes. She is correct when she says it is gross, may make you vomit or lose control of your bowels though.