Start Kenshi in Steam
Select "Launch Modding Tool."

In the top box, make sure all 4 of the game's base files are checked.
In the lower box, make sure Player Faction Armor Colors is checked AND NOTHING ELSE!! On the right are four tiny buttons. The bottom one is "select none." Do that, then click my mod.

Then click the TOP of the four tiny buttons to make a new mod.

Name it anything you want, like "MyFirstColorScheme," or "BlueAndGrey," or "Humphrey."
It should show up with

*ACTIVE*

after it in the line. Don't proceed unless your new mod is the *ACTIVE* mod. If it is, click DONE.

Then on the list on the left, click on COLOUR SCHEME.
Scroll down the list until you find "NamelessPlayer"
Double-click NamelessPlayer.

Click Color1. Click the button that appears on the right (it doesn't look much like a button, but it is! The silly button won't appear until you click the color!)
Ooooo, a color palette appears!
Choose your favorite color. This is now your faction's PRIMARY color.
Click Color 2. Click the button. I'm sure you can guess the rest. This is now your faction's SECONDARY color.
Click OK on all open windows.

Save mod.
Close FCS.
Start Kenshi.

Activate your file you just made in the MODS list and then click "Save Config." MAKE SURE YOUR FILE IS BELOW MINE IN THE LIST, OF COURSE.

Now your choices are your faction colors.

Starting a new playthrough? Feel like RPing a different group?
Wait, don't edit your first file! Make another one, with a differnet name!
Make as many as you want! When you get bored with one colorscheme, deselect it in the Mods list, and activate a different one! You can turn off a color plugin and/or turn on another one mid-playthrough, and all your armor will update - because textures are loaded when the game is, and the colors are applied when you load in. So if you decide your colors didn't come out quite right, save your game, adjust your colors, load back in, and there you go.