I am 6’4” tall and require a 1” longer shaft on all of my irons. If I install a new shaft that is 1” longer does it affect the flex?  Would it make a stiff flex react more like a regular or strong regular flex shaft?

Answered question

couple of factors here IMHO…
increasing the length will decrease the cpm (freq/flex) of the club and increase the Swingweight. To get the Swingweight back to wear it needs to be, you need to reduce the headweight (or increase the weight in grip area). This in turn brings the cpm (freq/flex) back up.
Also, if you take the club as is with the 1″ length increase and profile/measure the frequency of the club starting at 11″ from the centerline of head and thereafter every 5″ to a total of 36″ the frequency will be the same regardless of that 1″ increase.