They are absolutely NOT metric. But, if you go to many parts counters, they will have only 3 types of 3/16 brake lines. They will have:
1) a standard US line double flare 3/8-24 nut. (nut usually cad plated gold)
2) a (usually) Japanese line double flare 10x1mm nut(usually purple colored nut)
3) a (usually) European line SINGLE flare 10x1mm nut (usually blue colored nut)
The parts guy then assumes that the single, or bubble flare example you showed him is metric because that's the only single or bubble flare line he has.
There is a 4th line available which is what you need. Single, or bubble flare with 3/8-24 nut.(usually red or pink colored nut) Try a different parts store. I can give you manufacturers and part numbers if you wish. Bundyflex or Everco or Weatherhead are your best bet. They all come in lengths 8, 12, 20, 30, 40, 51, and 60 inches.
HTH Peter C.