Why is one of the blood transfusion reaction symptoms back and chest pain?

Those are symptoms. There can be a myriad of reactions to blood transfusions, from a simple fever to a condition called acute lung injury, which can be fatal. There can also be allergic reactions or, if the blood is mismatched, a devastating rejection reaction. Chest and back pain may be symptoms of those more severe reactions, like acute lung injury. If this happens during a blood transfusion, let the docs know.
Thrombosis. Chest pain can ensue for 2 reasons - blood clots in the lungs or in the heart leading to low oxygen supply to the heart muscle (a heart attack) or injury to the lining of the lung (pleurisy). Back pain in isolation is rare - generalized muscle aches due to small blood clots in the capillaries (the small arteries that caryy blood to the tissue) that lead to local muscle injury anywhere.