Besides fabric colors, I have shone the best represented colors in their pallet. I had to comb over many versions to find the most common colors, but this should be of help to you if you decide to use these colors with your costumes. Below is an explanation of them, and what they are for. There is NO REQUIREMENT to sue these colors, it is only for those people who want to get more fully immersed in the weekend.
Lapis Lazuli
Color for the stone. It can also be an Azurite blue if needed.
Egyptian Blue
This hue is far more bright and royal in feeling. It took great care and time to create this our for paints. It shows a sign of elegance and sophistication.
True Kaki
This is the best representation of the cloth possible. The original color was mixed from berries for the dye. This version has less yellow than the fabric, and remains more neutral.
Lead White
Is not pure white, but a cast of yellow. Depending where you find the sample there are many interpretations, but this also goes best with the main colors. It was chosen for being neutral and basic.
Kaki Cloth
The truest version of the cloth color after doing research. The cloth has a deeper tone, almost clay like tone to it.
Unbleached Cotton Poplin
Basic rough cotton color and texture. basic for the desert heat and reflecting off the sun.
Unbleached Muslin
Again a basic color and texture. The finer the thread count the better. It should be smooth and lite. The Egyptians did NOT HAVE pure white, so this is considered the best we can reproduce. It would naturally bleach itself in the sun, but remain bright and clean.
Chrysocolla Blue
This might be slightly more bright, but works well with the other tones and hues. I was thinking Organza (For modern times) as a Lady of the period would want lite, airy cloth but also remain stylish. Other fabrics can be used, but the idea is to keep it shear yer able to withstand sand blowing at you.
Ochre
This version shows a more subdued orange. Not bright or flashy, yet solid in hue and easy on the eyes. It also is a nice color when you need to go bright, but keeps the sun off of you to keep cool.
Egyptian Blue 2 or Turquoise
A brighter more fun blue that is used more as accent than anything else.
Malachite Green
This is used extensively throat the Empire, though there are so many version this particular one was selected as it went best with the others. It can be darker or lighter but again is used sparingly and in small amounts.
Lead
Is more basic yellow color. Bright and cheerful. It is also an accent color.
Carmine Red
The most basic of the reds, this hue is solid and works well with the other colors. While it can be used to detail it is also used to make things look more lavish than they really are.