Why does the fight or flight response use the endocrine system?

The fight or flight response uses both a neural and an endocrine response. The increased sympathetic activity will increase heart rate and contractility, divert blood from GI tract to skeletal muscles, cause pupil dilation, etc. The increased sympathetic activity also causes the adrenal medulla to secrete more catecholamines (mainly adrenaline but also noradrenaline and dopamine) into the blood. The adrenal medulla is made of up chromaffin cells, which are essentially modified post-ganglionic neurones, which rather than synapsing with an effector, just spills the adrenaline/noradrenaline into the blood (rather than forming a neuromuscular junction).