I am trying to dual boot with DOS 6.22 and NT 4.0, and am having trouble. Can I install DOS over NT (my original O/S? If so, how do I create the DOS system files?

It is generally assumed that if you use NT you shouldn't have to ask questions like this because you are an IT professional. I do realise that copies of NT are now falling more and more into the hands of common users, so I will give you this link: WinImage Bootpart.

If you already have NT installed, and want to add MS-DOS 5 or newer, make sure your boot drive is fat, and no larger than 2G.
make sure your repair disk is up to date.
from start>run type rdisk /s, this will update the repair folder, than make your repair disk just running rdisk (no switches).
make sure you have the NT boot cd, or the three floppies (to make new floppies, run (nt-cd):\i386\winnt /ox ). Boot from your dos floppy, exit setup, type "sys c:" that's the easy part, now the part thats tricky.
boot from your NT setup disk(S) (cd or floppies) to start setup. choose "R" for repair. !!uncheck EVERYTHING but "inspect boot sector"!!, again, uncheck EVERYTHING but inspect boot sector. continue, then your done. this process will fail if c: is NTFS, or is on a partion larger than 2G. if either is the case there are other, slightly more complicated options.