Just a quick thought, after looking at some at work online on youtube and such, Maybe you can get a long wooden dowel and add a hook that you can drill somehow in there and then sharpen or attach something at the end that is a blunt, but still pointed(maybe shaving or reducing it by sanding it until the right size). Then add a platform that has a small U cut, then a circle and finally a passage so your "dowel" can go through and then sit nicely in the "U" indentation on the plank. Attach that plank to another wooden board that is a bit thicker and have on the opposite end, sand or somehow get a crater or something so the end of the Dowel can sit in while its spinning. Finally Add something that is round or a fat donut type made out of something light but sturdy(rubber?) and affix it somewhere comfortable between the plank and the bottom so your feet can "kick" it. (also you might want do do something in the area where it will rest at an angle on the upright plank like decreasing the width of the shaft in that area and adding something slick on the "U". Hopefully this picture I tried to draw will somewhat make sense...Sorry just brainstorming at the moment. I am currently waiting for my spindolyn, but a kick spindle sounds fun. Good luck finding answers.
(quickie picture) :Kick Wheel Picture