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A thrombotic stroke occurs when a blood clot forms in an artery supplying blood to the brain. This blood clot usually forms in an artery that is already narrowed due to a buildup of plaque. When the blood clot blocks blood flow, it can lead to a stroke.

(A) Seizure disorder: Seizure disorders can have various causes and usually affect the activity of the brain, but they are not directly related to blood clot formation, which is the cause of a thrombotic stroke. (B) Influenza: Influenza is a viral infection that affects the respiratory system. It can cause complications in some cases but is not directly associated with thrombotic stroke. (C) Cocaine abuse: Cocaine is a powerful stimulant drug that can cause numerous health problems, including increased heart rate, high blood pressure, and constriction of blood vessels. These effects can increase the risk of blood clot formation and, consequently, increase the risk of a thrombotic stroke. (D) Childhood rheumatic fever: Rheumatic fever can cause inflammation in the heart, central nervous system, and other organs, which can cause long-term damage. However, it is not directly related to thrombotic stroke.

Based on the given options and their connection to thrombotic strokes, the most probable risk factor for strokes in this client's history is (C) Cocaine abuse since it directly affects blood vessel constriction and increases the risk of blood clot formation in the arteries supplying blood to the brain.