It depends on each state's laws. For Ohio, you must be certified by a national gun rights organization (like the NRA, USCCA, etc.) or be an Ohio Peace Officer Training Academy certified trainer. Then, your class must meet the minimum standards in Ohio law, consisting of a minimum of 6 hours classroom instruction (essentially, basic gun safety and firearm and ammo storage), a written test, and two hours of range time including live fire. The NRA Basic Pistol class meets those requirements as long as the time requirements are met. The only Ohio-specific requirement is that you must provide a link to the Ohio Attorney General's Concealed Carry Laws Manual.
If you meet those requirements, you can be a resident of any state and for that matter can teach in any state and the class is acceptable for an Ohio license. As far as KY, FL, etc, you'd have to find out what their laws are, I really don't know.