In golf, does the club shaft increase clubhead speed through shaft flex (shaft kick)? On the downswing, the shaft has a tendency to flex from backwards to forwards. While the shaft is in the process of flexing forward, it could increase clubhead speed (which would then be transferred to the ball). If so, is the amount of increased speed negligible? For example, if the clubhead was moving 100mph, what kind of shaft flex would be necessary to increase the speed of the clubhead to 105mph? Would it even be possible within human constraints?
ALL shafts kick forward at impact due to the conservation of angular momentum. I see no way to quantify "how much" the clubhead speed will be increased because there are too many factors, most of which are player related.
In fact, you could have a shaft which is too flexible for your swing, and it would "kick" too early, and the amount of increase could actually be lower than if using a stiffer shaft.
The only way to know for sure is to get on a real launch monitor such as TrackMan or FlightScope and have everything measured with different shafts. That's the whole purpose of club fittings.
Yes, this is one of the primary reasons for the graphite shaft being introduced. Shaft manufacturers offer a range of stiffness ratings so players can get the most benefit for their swing speed.
To quote wikipedia (https://en.wikipedia.org/wiki/Shaft_(golf)):
Shafts are quantified in a number of different ways. The most common is the shaft flex. Simply, the shaft flex is the amount that the shaft will bend when placed under a load. A stiffer shaft will not flex as much, which requires more power to bend and "whip" through the ball properly (which results in higher club speed at impact for more distance), while a more flexible shaft will whip with less power required for better distance on slower swings, but may torque and over-flex if swung with too much power causing the head not to be square, resulting in lower accuracy.