Make a folder for your mod here:
C:\Program Files (x86)\Steam\steamapps\workshop\content\301650\[any 9-digits]
C:\Program Files (x86)\GalaxyClient\Games\Battlezone 98 Redux\mods\[mod name]

This folder is going to contain the .dds texture files and a .ini file

Get a copy of the .dds file(s) you want from here:
STEAM: C:\Program Files (x86)\Steam\steamapps\common\Battlezone 98 Redux\BZ_ASSETS\materials\textures\
GOG: C:\Program Files (x86)\GalaxyClient\Games\Battlezone 98 Redux\BZ_ASSETS\materials\textures

DDS_DIFF for diffuse textures - The main file you want to edit to affect an object’s look
DDS_EMIS for emissive - where light is emitted – any colour added to this map will glow.
DDS_NORM for normal - texture
DDS_SPEC for specular - where the vehicle is reflective

The first two letters of the file name indicate the faction (a for American, s for Soviet, b for Black Dogs) and type (b for building, v for vehicle)
For example, here is the diffuse texture map for the Grizzly (avtank_D.dds):


Edit your new .dds file(s) (I recommend paint.net) and 'save as' using DXT5 compression. Keep the original file names.

Create the following .ini file in the same folder (use notepad and save as a .ini file). This will contain the name your mod will appear under in the in-game mod menu, as well as custom search tags to help people find it in the Steam workshop. Do not change ‘mapType’. In the example below the mod will appear in Battlezone as awesome mod:

Open UploaderApp.exe from here:
C:\Program Files (x86)\Steam\steamapps\common\Battlezone 98 Redux - Uploader Tool

or

In the Tools section of your Steam client

For your mod name use the same name as in your .ini file.

Select 'Create New Item' and select your mod folder (the 9-figure number).

Finally, you will need to select a preview .jpg. (This is how your mod will appear on the Steam workshop, you may need to create is seperately)

Good luck creating your Skins!