I mustr admit that the idea of holding milling cutters in a either a lathe chuck or worse a drill chuck does not fill me with enthusiasm. One of the problem I have had with parting has been when the job decides to start moving outwards in the chuck. If a piece of soft mild steel, maybe half an inch to an inch in diameter, can start to work sideways under the forces from a parting tool, what chance have we of holding a milling cutter securely?
I know that not everyone, especially when starting out, can afford the proper gear, but there are cheap alternatives. One that I have already mentioned elsewhere on this site is to make a holder for the cutter. This can be a taper shank to fit the spindle, tapped for a drawbar, and bore in situ for the size of cutter. A couple of grubscrews/setscrews at right angles will secure the cutter in place. (you can grind little flats where the screws will bear to be extra sure if you like.) This sort of things is actually sold commercially, but is not too hard to make, especially if you buy the taper shank. If you don’t have a taper in the headstock (the Unimat does not) another possible plan would be a similar holder, but with a parallel shank to hold in the four jaw chuck. This would need setting up with a dial gauge before use, but the holder being soft and a larger diameter should be able to be held securely in the jaws. It can of course be long enough to extend to the back of the jaws.
regards
John