I am having trouble getting dark black on a red shirt. It looks like dark burgundy... not fully opaque. Also, my artwork has a large field of khaki, and the color is reproducing as light yellow, very pale and WAY off.

Any advice for hitting black and other colors when printing on the white ink areas?

Sounds like you're using RGB, rather than CMYK?? The printing process they use on dark apparel is not very forgiving at all - try switching over to CMYK for your color choices before uploading the graphics - you'll be glad you did!