UTME83,
The .199" diameter is the exact sharp diamter of a #3 machine screw flat head 100 degrees. I do not understand your .395" number, unless perhaps that is the diameter. The sharp diameter of a #10 flat head screw is .385". A .395" countersink would sit your screw below flush. I am assuming you are using inches.
A #3 screw has a major diameter of .099", and they are hard to find. There are small solenoids on the market that use 3-48UNC tapped holes, and I am wondering what drugs the designers were on.
A 100 degree countersink definitely is English. Metric flat head screws are 90_degree. Most English screws are 82_degrees. Hopefully, a #10 screw will work for you.
I do not know the consequences of putting a 90_degree countersink screw into a 100_degree hole. It would look absolutely unprofessional.
JHG