Recognizing that there are several models/sizes of Sioux drills, here is the info off of mine.
The drill: SDR4P60N2
The Chuck: F6.5LBA
THD 3/8-24
Note, it is a 1/4” chuck
The chuck key: K7
If you google K7 chuck key, you will get plenty of hits.
One other thought, Brown Tool is a Sioux dealer.