I have two sets of formulations for red:
Formulation #1:
Shadow #1: Vallejo 70814 Burnt Cadmium Red
Shadow #2: Either Vallejo 70908 Carmine Red, or Game Color 72010 Bloody Red. If you want Crimson (officer's sashes), this is your mid color. Both are glossy, however.
Mid color: Vallejo 70947 Red
Highlight #1: Vallejo 70909 Vermillion
Highlight #2: Vallejo 70817 Scarlet
This produces a good British red. The burnt cadmium red gives great coverage over both black, gray and white primers, and that sets the rest of the reds up.
My other fomulation is for poorer quality red cloth or dyes, and is more of a terra-cotta or orange red. It's my preference for red uniforms for other ranks up to 1850 or so.
Formulation #2:
Shadow: Delta Ceramicoat Red Iron Oxide. This one has poor coverage of elevated areas, but settles well in the cracks, folds, and flatter areas. I like that in a shadow, especially over a gray primer.
Mid color: DecoArt Americana Georgia Clay. This has solid coverage over the shadow layer, and covers any bits of primer that show through.
Highlight: Delta Ceramicoat Poppy Orange
The other advantage of these is that you can find these colors, or similar ones, in just about any US craft store or Wal-Mart. They're cheap, too, usually $0.50 for 2 US fluid ounces, so you'll get a lot more painted with them.