Jesse,
As you have discovered, milling with drill chuck is a BAD idea. But, it is not absolutely necessary to go to the expense of buying a proper milling chuck. A suitable alternative is to use suitably sized collets of the type finger, direct, or MT collets (all names seem to apply).
It appears that the Clarke micro Mill uses the MT2 taper in the spindle and suitable collets are available at around £5 and use either a 6mm or a 10mm drawbar. Obviously I don't know what size your milling cutters are, or if they are suitable for use in these collets however, if bought as necessary, the overall cost can be spread around over a long period of time.
I'd also add that using a drawbar holds both collet and cutter securely.
Furthermore, if your lathe, assuming you have one, also has a MT2 taper in the headstock, then these collets can be used there as well. In addition, these collets can be used to hold material of the appropriate size, not just for milling cutting tools.
For information, both my milling machine and my lathe have a MT3 taper and I use these collets to both hold cutters in both lathe and milling machine, and to hold round material in the lathe.
Regards,
Peter G. Shaw
Edited By Peter G. Shaw on 16/01/2015 14:28:15
Edited By Peter G. Shaw on 16/01/2015 14:29:17