You flush your toilet to rid yourself of your bodies waste product, flushing your nutrient solution is also a good idea.
It is advisable, but not 100% necessary that you flush out your system before adding epsom salts. Reservoir , conduits the whole nine yards should be flushed and new [quality] water added. Run simply straight water and 1 tablespoon of epsom salts per gallon of water for 2 -3 days. Flush it out a second time and refill it with the nutrients you generally use.
If you are not ready to go so far as flushing and refilling and flushing again you can also try foliar feeding with epsom salts which has also proven effective in many instances. For foliar feeding use at roughly 1/3 the strength you would use when adding to the reservoir. Dissolve the salts in hot water, allow the water to cool to room temperature before spraying on the plant leaves. When trying to correct a MG deficiency I do this 2 - 3 X daily at least once during the day cycle and once during the night cycle.
Used in aquaponics, so long as it is not used in exorbitant amounts is actually beneficial to the health of the fish. It is sometimes used in aquariums to treat infections. For aquaponic systems add it directly to the fish tank in diluted quantities.
Recognizing Magnesium deficiencies
Leafy Vegetables such as legumes and beans or green leafy veggies and herbs will produce healthy yields when magnesium is deficient. However the yields will not be as good as they woulda, coulda, and shoulda been able to. Other vegetables such as tomatoes, peppers, eggplant or fruit bearing crops need higher levels of magnesium for optimal growth.
Magnesium deficiency is not always spotted until it becomes severe, sometimes too late. Common symptoms include stunted growth a yellowing of the foliage, leaf curl, and poor taste quality in the fruits - [sugars are not properly concentrated]- hence you get a lack of sweetness, a bitterness, and overall undesirable flavor in many crops.
After prolonged periods of magnesium deficiency, necrosis - Death and or degeneration of plant tissue occurs, which causes foliage and other parts to darken and wilt. You will also notice premature dropping of older leaves . In mild cases of Mg deficiency plants produce small, fibrous and woody fruits. Magnesium deficiency is sometimes mistaken with zinc or chlorine deficiencies, the symptoms are very similar.
Epsom Salts as Fertilizer Hydroponic Nutrients pH in Hydroponics