Such use is very dangerous. Perhaps using a drill press stand for strapping a reversing drill motor in would be better than an actual drill press. A reversing drill chuck is threaded to the shaft with a reverse thread screw internally to hold it in place. Milling machines always have a draw bar to retain the collets or chucks in place.
The Rong Fu Milling Machine Stand for Mill Drills 211/4" Long x 2315/16" Deep x 283/16" High can be found within the Milling Machine Stands category. As part of MSC Industrial Supply's Machinery offering, this item can be found using MSC part number 09519919.