I think the 3/16 is a British Standard Whitworth (BSW) size. It is very close in diameter to the #6 Unified Thread Standard (UTS) used in the U.S. and Canada. However, it has a different pitch.
3/16 BSW has pitch of 24 threads per inch while #6-32 UTS has a pitch of 32 threads per inch. So, it won't work. If you try to install a 3/16 in a 6-32 case tap you'll likely strip the thread in the case.
Also be aware that UTS sizes come in at least two flavors - UNC (Course) and UNF (Fine). #6-32 is a course thread and is often labeled 6-32 UNC.
There are other signifiers on a screw, and I think a fuller description on the Case Labs Tech Station foot screws is:
Steel, Zinc Plated (I think), Pan Head, Phillips Drive #6-32 x 1
The final number is length in inches.
A good mail order source is McMaster-Carr:
http://www.mcmaster.com/#machine-screw-fasteners/=g8rk2o