Hi Chuck;
I think your milling machine is a bit bigger than mine. The one I made, (in the link) is for a machine that only weighs about 75 pounds. If I'm looking at the right mini mill, it looks like yours weighs quite a bit more than that, so you might up the size a bit. Seems 1 1/2" dia would be reasonable.
Probably the best thing I can suggest is to use the fly cutter in a proper collet or end mill holder. It would be hard on a drill chuck, and might shake things loose. The largest practical shank diameter is what I would go for, and the shank short enough that it doesn't stick out of the spindle very far.
Dean