How many cigarettes would a person with asthma have to smoke in order to trigger an asthma attack?

Any smoke at all. You don't even have to smoke the cigarettes, just being around the second hand smoke can make your asthma flare.
No number is known. This is not known and any cigarette smoking can trigger an exacerbation. It could depend on type of cigarettes, style of smoking, severity of asthma and other factors. In general, smoking is not a good idea, whether one has asthma or not.