Okay, she looks like a fawn agouti, doesn't appear to have the rufus modifiers to turn the color into red. Her father is the same color, mother is a pointed white (a.k.a. Californian, Himalayan). Siblings are black and a black pointed white. So, let's look at the possible genetics:
Agouti, coded 'A' is dominant. Fawn is agouti so we know there is one dominant 'A', pointed whites are generally non-agouti, so mom would have donated a recessive 'a', so the rabbit would be 'Aa'
Black/brown is coded 'B'. The siblings both carry black, typical Flemish Giant fawn is black-based, mom probably has black points, so the rabbit would be either 'BB' or "Bb'.
The dad is a full-color fawn, 'C', it's unknown if he has a more recessive allele with that; mom would be recessive 'c(h)' (the 'h' stands for Himalayan). Since there were white kits in the litter, both parents must carry recessive albino 'cc'. Since the rabbit in question is a full-color fawn, we know she has 'C' from her dad, mom could only have donated either her c(h) Cal pattern or the REW albino as the recessive allele (allele is just a fancy word for a possible choice on any given gene.) So, she'll either be 'C c(h)' or 'Cc'.
All of the rabbits shown are dense color, not diluted pastels, she's at least 'Dd', and probably 'DD'.
The last main gene is the extension gene, coded 'E'. Of the five possibilities on this gene, it looks like only two are in play here, normal extension 'E' like the black sibling, and the non-extension fawn recessive 'ee', where the black/brown coloration does not extend to the body. In fawn, the agouti banding is simply fawn with white undercolor, no colored bands. Since the rabbit is a fawn, she must be 'ee'.
When you don't know what the second allele is with a dominant gene, we just put a dash after the dominant gene. That gives us A-B-Cc(h) or Cc D- ee for the doe. If the potential mate was a black, it would be recessive non-agouti aa, BB or Bb for dominant black, full color C-, dense color D-, and normal extension E-.
What could the kits be? Dad can only give non-agouti, mom could give either agouti or not, depending on her recessive. If she carries Aa, there's a 50/50 chance the kits would be self-colored. If she's AA, all of the kits will be agouti based, no blacks. There's a good chance the kits will carry black, not chocolate, unless both parents have an unknown chocolate recessive. Black-based colors would include black tortoiseshell, black, chestnut/sandy, fawn, Californian, and some albino whites.
Black buck would be full-color C-, the doe is full color C-, so if he carries an albino recessive, here's the possibilities. A Punnet square shows the possible combinations, in this case there's a 1 in 4 chance of a REW kit. (Sorry, mistyped albino in chart)
If the doe ended up with mom's Cal pattern, and the buck still has a recessive white:
In this case, there's a 1 in 4 chance of Cal pointed white kits.
However, if the buck has only two dominant full-color genes, he can only donate a dominant gene, and every kit will be full-color, no Cals or albino kits.
As far as the fawn recessive goes, we know your doe can only donate a recessive fawn allele. If the buck has two dominant normal extension alleles, none of the kits will be fawn, although they will all carry a fawn recessive. If they also get non-agouti 'aa', they could be blacks.
If the buck carries a recessive fawn allele, the kits will be:
That's a 50/50 chance of fawn kits.
That's a long answer to a simple question, but there's a lot of recessive possibilities.