Let's see. The OP mentions remembering high school physics, so should be able to follow this. Don't hesitate to ask questions if this is not clear. I will try to keep the response brief. First, average speed. As an approximation, a kettlebell travels along a curve that approximates a portion of a circle, an arc segment. Let's approximate this as one third of a circle on the way up, and the same on the way down. doing 10 swings thus has the kettlebell traveling along 10 X 2 / 3 = 6.6 complete circles. What is the radius of the circle? My arms are 28 inches long and the kettlebell handle and ball add about 6 inches for the distance between pivot point and center of mass, for a total of 34 inches. Since I am used to the metric system, I will approximate the radius of the circle along which the bell travels to .85 m. So, for a set of 10 swings, the bell travels 2 X pi X 6.6 X .85 = 35 m. A set of 10 swings takes between 15 and 20 secs, depending on many factors. Let's use 15 secs. In 1 min, the bell travels 4X35 = 140 m. In 1 hour, 60X60m = 8.4 km, so a kettlebell travels 8.4 km in one hour, or about 5.2 mph. Of course, there are a lot of approximations and assumptions and the real answer may be 4 or 6 and will depend on a lot of factors.
Now, that was probably not the question. The question seemed to be for maximum speed. Here again, we can get an approximation using physics. Once past vertical, the bell leaves the body and moves with no force except gravity doing work on it. This assumes that the force exerted by the arm is only radial, perpendicular to the movement and thus does no work. In this case, the potential energy gained by the kettlebell from bottom to top is equal to the kinetic energy of the bell at the bottom of the swing. Assuming that at the end the arm is parallel to the ground, and using the same approximation for radius of movement used above, .85m, we have g h = .5 v^2, with h = .85m, g = 10m/s/s, and solving for v: 4.12 m/s = about 9 mph.
Of course, this is all very approximative, but the order of magnitude is about 10 mph for the maximum speed. Also, this is good because it makes sense when compared to the first calculation regarding average speed.
I would be curious to see what video analysis would give. If someone has the right software, it should not be difficult to get a video from Youtube and measure the distance traveled by the bell between two successive frames. I also think that there exist devices you can attach to a kettlebell that include an accelerometer, and integrating this data would give speed.